{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Models for Regression & Classification\n",
    "\n",
    "<hr>\n",
    "\n",
    "### Agenda\n",
    "1. Simple Linear Regression using Ordinary Least Squares\n",
    "2. Gradient Descent Algorithm\n",
    "3. Regularized Regression Methods - Ridge, Lasso, ElasticNet\n",
    "4. Logistic Regression for Classification\n",
    "5. OnLine Learning Methods - Stochastic Gradient Descent & Passive Aggrasive\n",
    "6. Robust Regression - Dealing with outliers & Model errors\n",
    "7. Polynomial Regression\n",
    "8. Bias-Variance Tradeoff\n",
    "\n",
    "* Link https://www.slideshare.net/zekelabs/linear-regression-114293440\n",
    "\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Simple Linear Regression using Ordinary Least Squares\n",
    "\n",
    "* Feature consist of p independent variables (p-dim)\n",
    "* Target/dependent variable is represented by y\n",
    "* Relation between feature & target is represented by the following equation\n",
    "* w's represent weights or coef's for each feature, w0 is intercept "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://github.com/awantik/machine-learning-slides/blob/master/lm1.PNG?raw=true\" width=\"300\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Residual Squared Sum (RSS) of Error - Sum of square of difference between actual value & predicted value\n",
    "\n",
    "<img src=\"https://github.com/awantik/machine-learning-slides/blob/master/lm2.PNG?raw=true\" width=\"500\">\n",
    "\n",
    "## 2. Gradient Descent\n",
    "\n",
    "* LinearRegression tries to minimize RSS using <a href=\"https://www.kdnuggets.com/2017/04/simple-understand-gradient-descent-algorithm.html\">Gradient Descent</a>. \n",
    "* The objective of Gradient Descent is the obtain best weights such that RSS is minimal.\n",
    "\n",
    "<img src=\"https://github.com/awantik/machine-learning-slides/blob/master/gd.PNG?raw=true\" width=\"500\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Feature Transformation\n",
    "![](img/1.featureTransform-01.jpg)\n",
    "\n",
    "### Understanding Math behind gradient descent with simplified notation\n",
    "* Prediction, $y_p = Ax+B$\n",
    "* Actual, y\n",
    "* Simplified Loss for caclulation, Loss = $1/2 *\\sum(y_p - y)^2$\n",
    "* Algorithm \n",
    "  - Randomly initialize weights A & B\n",
    "  - Calculate gradient .i.e change in Loss when A & B are changed.\n",
    "  - Change weights by gradients calculated & reduce the loss\n",
    "  - Repeat the whole process till weights don't significantly reduce any further\n",
    "  \n",
    "![](img/2.gradientDescent-01.jpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Genrating Regression Dataset\n",
    "* n_features - number of features to be considered\n",
    "* noise - deviation from straight line\n",
    "* n_samples - number of samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_regression\n",
    "X,Y = make_regression(n_features=1, noise=10, n_samples=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x204167dbcf8>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20414684c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Feature - X')\n",
    "plt.ylabel('Target - Y')\n",
    "plt.scatter(X,Y,s=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Hyper-parameters are initial configuration of Models\n",
    "* Initialize LinearRegression model with default hyper-parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = LinearRegression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Common Hyperparameters\n",
    "* fit_interceprt - Whether to calculate intercept for the model, not required if data is centered\n",
    "* normalize - X will be normalized by subtracting mean & dividing by standard deviation\n",
    "\n",
    "* <b>PS: By stanrdadizing data before subjecting to model, coef's tells the importance of features</b>\n",
    "\n",
    "#### Common Attributes\n",
    "* coef - weights for each independent variables\n",
    "* intercept - bias of independent term of linear models\n",
    "\n",
    "#### Common Functions\n",
    "* fit - trains the model. Takes X & Y\n",
    "* predict - Once model is trained, for given X using predict function Y can be predicted\n",
    "\n",
    "#### Multiple Target\n",
    "* Y can be of more than 1 dimension\n",
    "* Advantages of multiple target are \n",
    "  - computationally fast\n",
    "  - model is optimized for multiple targets\n",
    "  - model do not use relationship between targets\n",
    "  - model is more interpretable\n",
    "  \n",
    "<hr/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training model\n",
    "* X should be in rows of data format, X.ndim == 2\n",
    "* Y should be 1D for simgle target & 2D for more than one target\n",
    "* fit function for training the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.fit(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([31.36482038])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.16344907235574668"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predicting using trained model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred = lr.predict(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Blue dots represent maps to actual target data\n",
    "* Orange dots represent predicted data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20414781eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X,Y,s=5, label='training')\n",
    "plt.scatter(X,pred,s=5, label='prediction')\n",
    "plt.xlabel('Feature - X')\n",
    "plt.ylabel('Target - Y')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Limitation of Ordinary Least Square Technique\n",
    "* Impacted by Outliers\n",
    "* Non-linearities \n",
    "* Too many independent variables\n",
    "* Multicollinearity \n",
    "* Heteroskedasticity\n",
    "* Noise in the Independent Variables\n",
    "* <a href=\"http://www.clockbackward.com/2009/06/18/ordinary-least-squares-linear-regression-flaws-problems-and-pitfalls/\">References</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Regularized Regression Methods \n",
    "![](img/3.RegressionTechniques-01.jpg)\n",
    "\n",
    "### Ridge Regression\n",
    "* Ridge Regression imposes penalty on size of coef.\n",
    "* Less impacted by outliers.\n",
    "\n",
    "#### Adding outliers to data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge = Ridge(alpha=.1)\n",
    "lr = LinearRegression()\n",
    "ridge.fit([[0, 0], [0, 0], [1, 1]],  [0, .1, 1])\n",
    "lr.fit([[0, 0], [0, 0], [1, 1]],  [0, .1, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.44186047, 0.44186047])"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.47086948e+14,  1.47086948e+14])"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "outliers = Y[950:] - 600"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "Y_Out = np.append(Y[:950],outliers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x204188fc7b8>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x204167be518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X,Y_Out,s=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.fit(X,Y_Out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred_Out = lr.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Linear Regression')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x204188da828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X,Y_Out,s=5,label='actual')\n",
    "plt.scatter(X,pred_Out,s=5,label='prediction with outliers')\n",
    "plt.scatter(X,pred,s=5,c='k', label='prediction without outlier')\n",
    "plt.legend()\n",
    "plt.title('Linear Regression')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([24.43755395])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Ridge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "ridge = Ridge(alpha=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=1000, copy_X=True, fit_intercept=True, max_iter=None,\n",
       "   normalize=False, random_state=None, solver='auto', tol=0.001)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge.fit(X,Y_Out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred_ridge = ridge.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Linear Regression')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20418a9cb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X,Y_Out,s=5,label='actual')\n",
    "plt.scatter(X,pred_Out,s=5, c='r' ,label='LinearRegression with outliers')\n",
    "plt.scatter(X,pred_ridge,s=5,c='k', label='RidgeRegression with outlier')\n",
    "plt.legend()\n",
    "plt.title('Linear Regression')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12.48729023])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Effects of alpha using Ridge on Coeficients \n",
    "* Data generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y, w = make_regression(n_samples=10, n_features=10, coef=True,\n",
    "                          random_state=1, bias=3.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([80.71051956, 10.74941291, 38.78606441, 13.64552257,  5.99176895,\n",
       "       86.35418546, 12.13434557,  4.45518785, 74.71216427, 55.6240234 ])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training Ridge for different values of alpha\n",
    "* Coefs calculated are appended to a list\n",
    "* Generate 20 alphas from 10^-6 to 10^6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.00000000e-06, 1.14895100e-06, 1.32008840e-06, 1.51671689e-06,\n",
       "       1.74263339e-06, 2.00220037e-06, 2.30043012e-06, 2.64308149e-06,\n",
       "       3.03677112e-06, 3.48910121e-06, 4.00880633e-06, 4.60592204e-06,\n",
       "       5.29197874e-06, 6.08022426e-06, 6.98587975e-06, 8.02643352e-06,\n",
       "       9.22197882e-06, 1.05956018e-05, 1.21738273e-05, 1.39871310e-05])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alphas = np.logspace(-6, 6, 200)\n",
    "alphas[:20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "coefs = []\n",
    "for a in alphas:\n",
    "    ridge = Ridge(alpha=a, fit_intercept=False)\n",
    "    ridge.fit(X, y)\n",
    "    coefs.append(ridge.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plotting alphas & coefs\n",
    "* Different colors represents different coefs\n",
    "\n",
    "#### Conclusion\n",
    "* As alpha tends toward zero the coefficients found by Ridge regression stabilize towards the randomly sampled vector w (similar to LinearRegression).\n",
    "* For big alpha (strong regularisation) the coefficients are smaller (eventually converging at 0) leading to a simpler and biased solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20418d4a978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.gca()\n",
    "ax.plot(alphas, coefs)\n",
    "ax.set_xscale('log')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('weights')\n",
    "plt.title('Ridge coefficients as a function of the regularization')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lasso\n",
    "* Linear model that predict's sparse coefs\n",
    "* Reduces the regressors predicting target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Lasso(alpha=0.1, copy_X=True, fit_intercept=True, max_iter=1000,\n",
       "   normalize=False, positive=False, precompute=False, random_state=None,\n",
       "   selection='cyclic', tol=0.0001, warm_start=False)"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lasso = Lasso(alpha=.1)\n",
    "lasso.fit([[0, 0], [0, 0], [1, 1]],  [0, .1, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.5, 0. ])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lasso.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Elastic Net   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Elastic-net is useful when there are multiple features which are correlated with one another. Lasso is likely to pick one of these at random, while elastic-net is likely to pick both."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "en = ElasticNet(alpha=.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ElasticNet(alpha=0.1, copy_X=True, fit_intercept=True, l1_ratio=0.5,\n",
       "      max_iter=1000, normalize=False, positive=False, precompute=False,\n",
       "      random_state=None, selection='cyclic', tol=0.0001, warm_start=False)"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "en.fit([[0, 0], [0, 0], [1, 1]],  [0, .1, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.32589556, 0.32579954])"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "en.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Logistic Regression\n",
    "* Linear Model of classification, assumes linear relationship between feature & target\n",
    "* y = e^(b0 + b1*x) / (1 + e^(b0 + b1*x))\n",
    "* Returns class probabilities\n",
    "* Hyperparameter : C - regularization coef\n",
    "* Fundamentally suited for bi-class classification\n",
    "\n",
    "![](img/4.LogisticRegression-01.jpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_blobs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "X,y = make_blobs(n_features=2, n_samples=1000, cluster_std=2,centers=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x22ebc4c9588>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22ebc2eb128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0],X[:,1],c=y,s=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "h = .02\n",
    "x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n",
    "y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
       "          penalty='l2', random_state=None, solver='liblinear', tol=0.0001,\n",
       "          verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "lr = LogisticRegression()\n",
    "lr.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = lr.predict(np.c_[xx.ravel(), yy.ravel()])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x22ebc571b70>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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qp8CbgRpr7ZzI9/KA3wClwEngQWttw5XcZ9Jthom3WNrrYcf/arpa5BcqZ4KNhRFkNTrwgo9VhLvjxMxKKGIgyBlvY8Kh/RJKsUZCKdW7LywG1igOPOXjQNz3UrJF7OVxmPlm6XmrtQj+zv/TWCO7CpADwabK89wgYkes4rQ0kOaFkKLUHIDF7zeYkLwH8FJCJ91mOLvfx5IPGrLHiggv+ZDhta9oyp73cXZfpNHIMfplUTDvHSa24wAZW1p+7+cdfkGx4N0WY6CrCeouIZQx6VYRe+2XQ86JNxsOv5A4oXQ0yH11XJZT9H3njIeag+e//om1mhNr+z8eh2MgGKilxc+Be3p874vAK9baqcArka8vm5wJlml3W1JzILcU5j/kpZZVbteEuollj5zdPziHfkdeEtEPdkqMe6Di97VlSlIbjaRjlj0voZgtP9bUHLz093LkZUUoMs7WGvledAKQvq1yPnDwGUVDhRziHf5j3/8U2usVJ9ZGJiErf6q4yaS1Bvb9XipjxVDMSxcF+XlklcDdXwmTOTpuxW0gJUf+2lihqD/S/3aFSRlxE1pkTMEO2XHFU71Hs+brmq2PaNZ+U19SgVRC+ilg+5iItvxQU3dYGqTUHZZ/fyCfj3TPGiok+0cHhk9ChmN4MGBZOkqpUuDZuBV+GXCbtbZaKTUGWG2tnX6ha1woS2f0XMv8d5lY9kdzFaz9hrfiyplgyRlvqT+qaKm+NJH0J1sWvU/ylM/sk8KU860000dZUnMjufADWGGZM8FSMM3SUK6oO3z52R9puTIZpeRIBk9zJSSlK5Z9VBSsu136ttYfVRx5WSW8z5wJltKVhrZaxbFXVUIaZMYYw02fsbGDRmulyGvzDzXBdsWd/xSOhUyCnXB6qxSIJWd77p3WRETRyhhPbVE0nrp0X/2C6ZbFHzRgpPAs2pTFhGH9dxVNp698HRNIs9z4l1JY13IWNn7/wkV1OmCZeqchPR9OrNMDEuq7HJSWnPv8yfJ5b/mR5tyJ4Zv15BgYhkOWTpG1thogIvqFV3Kx2jLoapG/aw2HX0r8R9xYri7ZXTLK1LsN+VNkdVq8AM4dt5w+T6VrW526/Hx7ACxZYy2z7pfdyvE1ivL1+orGDxI/X/FJQ1YJYOHMXsTRUUHtIctrX1UUzZaMkLRcyJ9smXizZetPpS9tap7lho9Hsme6Lam5lj2PexNq5zkvhmOMOHG+/m3v8fINikm3WbDQ1QwHn9GU+eGuf4lbKiv5GZZvgml3wdS7LSZk2fO4omqHJ9JJGTIBZxTAyfWKo39KFPDaMsVrX9GkZMONnzJeKEXD8octL/2D7bd7pS9JrI7TCwzjlknR265faVprFGu+7kMHbL/SbU1QUfb80Kc6jpoKeaXe2czsBwzrvjn043IMD4b80FYp9TDwMEBB2vmHE+5WrP2GJne85G631w/cqiUlyws1aB9eJssgMPdBw/hlgJJV6cz7LI3ltlda5MXQAcu0NxoyCyUe7AtA1hgv1a9ksRfjLpoDGaMtldtUQnw9KR2WfcTw4t9qssZ4YQxfEuRPTrxfqFsm3cJZIop7fgvZEwzhLvlZHH5RU3/UkpRhqTkkHvGlKxMrOpWSmPe0OyPpoZEU0eIFlqodcZ/R2w15pRI/n/IGy7njNuZTNPn2MJNXyRh2/EJTtVMOT1Xk8/SnEumQ1Y/P0G+5+fOGlGzPhsIaWPJhw+qvyj+Iy6mtmPwGw4QbLM3VMnlczeYpJkQsi9eagUtxdVwbDKbgn1VKjYkL6dT09SRr7Y+AH4GEdC50QRNUvSoxB4Jjr2mKZklRlQlB5bZL+QW1FM6SUM+Zvb3T8ZIzLQvfK1v9is1irRuf4WKNHLI2ne7f3cYtN8y4V9JDo6X2BdMNNizhDZAVOMQdairJUOlsiWQBae8xaS0YSVdUEXuHIJw9KAeXoW44vUVRskRyzn1+UGmw/GF5nTXQ3WZZ9y1N/bHEmgETjkwikck0vuI3GkkMdRF5nTiGjl9hyRnvHfzK4bhUBY+/McyMe73JaulHDH/6J03uRPEDsgYaTkKoq5/58CWQnJVo/qb0RQ7j1YV3D6Omehljydkw+62G3Y9dvRV2/TGo2gnjlomL557HXQaQw2MwBf9p4P3A1yJ//mEQ73VFNFcqXv2KJm2UHLaF+ykYICl4U++UNMVpd1tWf83LHgLJBc+bKDuHybcnpixaKznndf0s0U/Jscx5q401MY8SnyFiLXQ2QmM5jJ7nibvS0kHq9W8rFrzbkD0u8nwDU++SjJbXv6UpXmhpb7BMuzsitFbM2RpPxe0OfIkZMknpMH6F5ciLiZ9bQzl0Nkc8h1Tieweo2iUCXXcYkrMMKz5hSc2XKcMY8asJthM7uJ6wIvEaSWmSDhlNvwwbOLtPHtM+S9FsOTOoOSSVvKUrDd0dihNrpaK4M65hTNSCAhs9jE+068yZYFn2EYM/BY6vhkPP9S3i0hNA8Pn7zh4aXBR7Hvex57f9D2s5rh8GKi3zMeA2YJRS6jTwD4jQP66U+jBQAbxjIO41WHS3qT6bgl+MksVeSqgJQ94kKf6KkprribHPLwU6aXmygpWCIdXvCSaQ2sOkLELCJBJZ3RfNEdfMYIcU9jSegps/bwh3w6FnYWYRBJIlbXLCCsvhF+R84sjLirRRluQMz66hYDrsf1Ix6RZLmMiKuMc9Qz0arI+Zb1jwLhubJKxJfE1bLez8peKGj1umv1EKwJQvceLa/qii4aQi3K3wp0iIJHOMhIKsFS+j/EleHwFfQEJOJ163rPgLQ+ZouefZ/TBqmqST2rAlf5Jly499dDaJIdu0ewwmLPbLvoC83/ErLBUbvQEveJeJGcuV3gyVO2yfyQFnDyhm3GtjqazHXhmiFbYTe0cfDIjgW2vfdZ6H3jAQ1x/ONFZIpakvki3S3qOt4JGXFPMjwqe057CplGSvLPxzywtfspGURMuUOyzFCy0NJ2H/E4mGYS1npFCn1wo/GrO1UL5BtvNRsUZJ5sqqL4kw+gIw+23exGDCIr5RUnIsE1aYWHjHGmlq0l6veO3fNNljwRjL3HfYWKenUBdMvdOSlh9m/1OS4TTptsSdiEUmn0CqjDclG8avEP/8+AnThOXJbfVQd1gTSLes/HSYzMgZQ8sZEfzT2+DYqz6yx1mimWahbincyiq2ZBV7n1PxAnlMa0AnOnJGewRPeYMhZ5xcJ1rlXLHRe140XBZ9M/o8vznBNsXqr2lyS6G9TibRq4H2SSisq+Xq3dMx8hjyQ9uRzr4nNMF2aUiSUQgrP2Upe8Fw7FVZ2VXt0qQXGabcbvEFInnqPSyClU/EbPRcOaT0J0N6PnS3Gsr+6IUOCmcqUrJsgsDH/72rRfL3SxZLsRERL5tovnsU7YMDz0LxIhlPewPklBqaKy2rvuiJW3crVO+GshflvXS3qUi4Q7H63+Q58x4KM3axCOC4ZRJDPrNHJpHscV6+fHSCiy9c0z6bsKJvb4C6QyL6RyMr43nvENOw6A4goxBe/RcvbNZcBcdeVeRPEcErWSS7ruhnbIw4gPoCkQksDOeO9/451h9LbJh+pkctx77faxa/X2bJmoPQdOq8/yQIdSpqD53/8YFG+y0rPyvnGFrDnt8pKre52L2jN07wrxQLh55TTLzZE6/p91hOrjdovyLUCac2yeMmLKv72jIojFQknFjnZYKkjbKxilZfEmSMhrFLDRNWim99IJVePmrWxO0Y0sQzZsN/aqbcIc0uDr+oSc3p7X+u/YrGcsu45ZLdU7LIEg5G8toj90jKECG86TOGlCw4+bp09oofREq2t9r1BSAtV05p9z2hySiUs4KYyEeyYIyR7JyZb/Zi6EpBchoJTVNAYuDxISulvENpsKz4hCErUr2rNKgkuceZfXJQHe6OOHAamHSLoasNjq/uLYYNJxVbfqQpnGlorOjtSFlzQPHS32sCaRallLiEDhNb+byJkJ5HrOfvtLstlduGdkyO4YkT/MtE+yzLP2bIm+R5yEdRPrj9by2BFBHRTf+jWf01Tf5kCUnkTZQiq3AQag564nNmj2LqHTaWSdNwXDHnARvLaonaGURXr2218kueHOnC5PNLFtCBp1SclTEseHfi+GwYGsoVc9/mFVIpJemMPc8IFr7XopDxTFgpQtpw0nu89ayiYHrUhA3ypkL22DDZY+HUFin0KpjuHdpaIuKsAJ14P38KvbJgzp3wjNushZZaYp42KdnEzNHAu5YJQdMpxdFXNMmZlhs+aUgviBwGh6H1rOXMnt5hj3PHFY2nNOkF0rc3mk7pT5ELJ2fAjZ+2+JIsnY3w+neubsrl+ehqJVYzbyM2Eg5HXzjBv0xKFltZvWpJv2ssh9wJxPLroyZi2g9z3mpY/58+qndLmubst0p4x58s/jMv/4MoVnu9Ys3XNbmlciCYPzXOdz4uFBLshBNrJewxeo5h0fu8cemATEZob+dgQsSSTqyF+hOSPuhLEusDHZ91o7zJpVdmjfVWkVG6WmQCUZF/SUUzIqKuJftn92OKzNGWlOw40e/j4NnaSAvDHoeNPUMnSXH3N+FEEzeQrJzaw1LQBrDoA5E2lNGDXQ2L3ms5szfM3t9JlXDs2umWm/9KMnGw0vOgYJplxr0y4OZq2UVpLYfx45ZZTqwdesFvqRabjKl3WDoaxSvJ4egLJ/iXiU6KMwlDVvk1h6BwBr0yWLQf5r4jTMc5RdUeYt2HoPcBbGeTimX5hEMw495IqCV6Ly3piJNXwbHVNpZeCZE4fjPc/VWD1tKVaecvFAeelokBRPhGTYbcCRF3TpP4+p4iHxXncFAEr6cBWc0hKF0p5wTRVX4sgqMgkC5md8kXMZoLByV/PJAqTpjpoyT9se6owhobSwUNpHmvCXZErKED3v20T9orRr3pMwt7TFrIc4rmgPYbtv3U2wmVLBa3z6gf0JQ7DWPmejuI7BJib077E8cy1JSv15SvH+pROIY717zgK22Z83ZD0Uw5UNz9694dlTLHWGbeJ6l5B57S/arizRlrE2LTNWXST9ZMAbSkQialSWZKeoGEJUxIXCurdkPxfHndwWd63stSssSSWWSp3q1Z+x+aUdMsnc2WpR8iIca/6ouWYHuioMXHvHMnwO1/Z+losAmTEMqryFVyy1h83ZJYmKWUHGLu+KWi5oDyVuDKcNsXxS4ar2OivAMr798amcCyS2yCe6e1xMI5JiiC2lIFVTs1N35KHDWVgpn3w/afW0JdsrOwYdlJZY+zTLvL0N0GR1+GSbdAIN2rN8gohJs/H2bLjzW1ZWIDHb+ziIa/MosSP/lghxeXt0ZqJOJ3Izb6MUbeZ84EZ07mGFlc84I//gZLySIRuNFzoGWV5ejLnvppn+RsB1JEs7KKDa/+y8UrI9PyvQPHcDdMuV2Ke5SWMMer/ypL5fzJlsXvl9CDL0maSL/yz5ojL8nr4ou0ACa/QSo1fUlQepNh/1OKccslzRAiB55xh7TJGX2vzMH7OjU38fvWes6ORLJ70vKg9hCUb4SlHyJBvAHOHYsTeyw3fc7rDUCcmEa7bmUUyPfHLbdefDmur2psLOKBxvG1kvueOTrxfeRPgfX/qZl8mwj8yfWK2/6fhF2iE5QJyqTkizNSyyqGmz5rOL5GcvCT0r3nRQ+mT6xL/MAqt8t5RNFssYsue17TcNIy70EZeMVmGLfUqxS2zrbAMcK45gU/OSvRaz41J3FVFkiLEwoinawuUj4PcHyNJnucWBqYsKRRRieAQBqkZIvNQnMlgBTihEPiGw+K9vq+r1u8INHbf+7bbELOd9QnX/u8XPueq9eEtM+4uHnUtrh8o1hKZ4+11B1VtNUolDas+AvLoveQGJKKFEBFDyfTRknbwOyS3hNM9Pnxol04HU5vl1V2d4tk/sQXbgVS5c+Ff04sdBOfbnpmj4wvauSWVWyxkZhY9GemkyP5+yRmBKXmwox7ve/rAITbxf0y1AVJmeL9092qIp+tYucvEyf7yu2Kyh02do20POnJ290CB/7gYuWOkcU1L/int2om3uzFr0+uT/wl7WqB5kqp4IRIjLofVYpn90mrvoxCqD8uJmRZEREMdYilAEju+uvf1oxdKi39LtSuEETIY4L8efzdAAAgAElEQVTXxwGntRJ6iB4K9xT3hNz8aIgmLkNG+UR8KzZJQ2yQsFfupIj5Wop3H2vg8IuK2kOajEJLyRLD5FWJIZ/451orwht/LqH8nrlZWr7sLIKdXgEWRDz2lZf/335O3uOx1xT1xxJ/Xq01EmpR2vMSkvcQ977jPgNfwJsMAFKzvPaURbNg3BJDxWaZhE6s690mUS6oYtfd+hMfymexYUiMkzkcw58B88MfCC7kh38lBNIlJNJSTWw1F4/2W8bMkzz5M3v734gjHn+KNAr3JcGJNZrOpssTgwV/HqZkoQhYOOgd+iYYrtnEBiB9rbSjj8UTL4jnTsDG7/vIn2JZ+mET20XoSBFYczW8/m2NNYpp9xgmr4pUC/cQemMiq2yfVLMefhGm3xNXYGbplUnTczfS0SjnHf5IC8bja6Fio6azEfoS1UCaje2EJq2yvSa/+Pdpw9DeKDuw+McS3kMkDTbYDq/8S+8zHodjuDMc/PCHDcE2Rf0F2tuZkKJyx5X9koc6VawFXm6pZckHw4SDsPe34q3eXw49p8kdb0gbJS3/9j4hBUrRblJReopb/PeiJAhf3MSglDdhzHvI9LI2MCE4+Gx04rNMeYNNiLvH30vHrax15PyiuVp63GqdkJDU59iwUL5ezjKiHc2m3gFTVhnO7IcdjyYWegEE2xXlG+R7vmSZjKKZNdGdURRjpCgp/rPo+blFP1dfkoSB4q0mHI5rCReE7AdJGZbssVby2y+CDliWPyzds/ImwvKPX1o5ps8PZw9IBW5aPtz6/yT0oP2JRVfxYRsQoT61BbY+IvYKwR5GcNHYv43k8e97MrpF8J4Tdd3UAVj2EcuSD4Xxp0h4JeFa1hPXhCpYH8x/EHLGxrVUJGK5bBLHH/vTQOMpTf1RRXKWF5rRfpnkskpkkKl5Fn9y78//6CtiY9DdluhjFLVR8CfJNePvF0/8+YYvCW76jKFgxvDZ9TocA8l1scK/EvKnSsgDAx1NEuaItjZU2pI3WVIQm07J95LSvNRJpaUadNH7w5xYc/G2d4FUy02f91bcfYUf+rIZaD4tHacqNsnyNj3f4E9NnBy0Dw48A9W7FF0tChsxZdvzG83Sj5iEuHtUrAumw8z7DVsf0Sx/WDJjVCR9M15E43cO0QKs+Mwha+Dlf4BVf+Plrkdf09UK9UcUKdk2YZKIjsOGLTd8wpI7QeambY9o6o7Ii0sWG8bMk4PnbT9TpI2ClZ8Wl8/uVi/3P9pasTtiRV08P9EDXwbkZT4tfp9hz+OKtnoV+7k6HNcCI0bwixcaJt9uaa+DPb9NrJAcTGa80cRy1lMVFM2yVO1SBDIMyz9qY+mHx9coDr+g6WyK5IqP9Q4hi+dD4QzD7l8rpr9JVLLs+WiBlfc+CmaK2Pcl9NGVuAmT4EdvLZzepqjYJGqpA5aZ9/UOwSgFM++VVMKag5BeYGksF6+c9f+pWPlpLzsoKta+gIRDGssVa/5Ds/JThuRMYnnx2hc5ED3PgWl0RR9sBxMWi+P49xYOQn2kF0Bnk+LcCXGyjK66Gysgb7IlZ5x3EDznbYZTmxXJ2ZbxN8gKftQ0saM4vVVRtQNKlsq1j74iVhPdHRKmSR8l18yfFNnNxP3rTwjxJMPcBy1KW/Y9oTi9xW2EHdcGI0LwM4os8x6SytCMIljgN2x95Op0Eepq9dIgAbrbFQUzLEs+mHiIOelW8ZQHxab/0RTMgPkPmVhjb2tgwbs8y+BF77PUHLRsfUSjFIxdZph1f+K9rZVc/c5mMVyr3K4YM89SvFB2DiYsYYt4Z8ZxS01shxG9Bnir/Jn3W2a+2cbi9fueUNQdIWa7HL8qD4fgaMT1s7NR8cpXFOOXWcaviFSdIvev3i39cy0i7oEUqNwRWUVrKHtOE+5SNJ0Kk1kcZ3SmZVJMzRW30ZpDkraZlC4TSu5E+S/2XoyEuaa/MZImGXmf/mQYNV189aMHuIEU6Zt79oA0hBm3TN5f5hjY93t5v9njYMob+s44ijZen3SLpWhWmLyJMlHueVwOsvMmScP31jrF0ZeVd9CrLClZssOIt7Z2OIYDI0Lw0/K92KvPD+lX1A790jixTpFbagmkyKpx4i1iQ5twgGq8BuvytaLmAFRuF8/3qP2xik9XVNI3NmccTLrNyKFsUuLquOMc1B0TUTbdIrzjbwh7Pj0+KVpa9rCkowTSel+j/gTkTfDEUfsk7OKLPD7/nZZwF+x7UkzWojUL7Q2w+b817efkYtljLTf+pU3whTdhaeiy57eaXb+SvrnLPyoTYXoB7P6Nor1Ok5Rhmf+uMN0dcHqrpGn6I7bQhTOhcIZNbH7SYxcTfS8mTMIkG91BmKDk+8e/9+jh7aipsrqPTrS+AMx9u+xSGsoT6xRAnpuSE+mgFSlOix6Yj1kADeWWuiOw7GHZ+YW7LSmZ0vDdl2S58S8NGUXy2g3f07SedaLvGD6MCME/d0zi5CCrwqtlWJWUISt5fxKgpKq1YLqsuqMVr9ZKbvi2n3vbfl+SpfRmSzgMB58FX0Bx9gDc/DmbmMOuRHgKZ3lWB7HwTSRvvSQLfD7Lzv+Tx9PyEwuufH7JLOmZhQIyyXS3RHLk+wi7KBU51ETOHmoOSjUyFo6vVjGxB1j0PtPL9wcFG3/gtYSc/6DsaFSkycitX7AceiHMzHu9w9iemUTaJwLvi/+X2MfmLTrB9XwPUdGPt3VOyEjSUjWbVRJ3+YBcK2tM4vWNgfXf1RTOtky61dJ6Rr6XOdoba3IWvRq+RxuqFC+0pBd4159xb6JXj8Mx1IwIwQ91iYtkwXRLR4OShttXgYxCeuWRax8EQxJmSc2Bk+vhUA+P+KUfMuROlNd1t4nNQt6kSCVpnCgdfUXRelaqcXMizpvGiOdP7ngpTvIFxAI4yvHXNDnjTWyl2/Mg14S8cVoroZbzWS7Ei2Znk2LUFM/meOZ9llObbSxUkZLdxwekYNrdcOCpyD0D3melFKDl3CD+PCH+3iYI5Zug9MbEy5oeGUDR0FavCSdCfFP0nmcI5Rv7nhBNOPIzjLOdCHVKqKdym475yWeOsYyeKxVs1kpD96j7aDSFtWqXXNzEWS1Y4uwrhiH+FEt2iSxWetp7OK5dRoTgg+S5x/eKvRq0VHvpjNGGFyYkFaDHV2tQNrLaThxX7kRvFe5PhtQ86Gggob9r/XE4+rKo49ZHNNPuNiSlieVxVwvc9jeGcEhWv1W7vGvXHFSs/YYmZ5ylYLoczjZXi/BaI92ctjyiuPULNrYyjWKtxLOT0on56YSDULlNUXMwMXNFa7jpc9LHteyPkRh/IPF6Skko5UDk6/1PSjZPNBwTLeLqCxOCl74sGU9ZY8LkT/Emn1BHZMeTFAkb1ch/Y+bKR92XuEdfGw56u6VwN1Tt0ORNkv4D0YnBGLFdPrlekTVGvm9CcHxN759lS7Xita9oMork30OwQx5f9y3NmPmW9nOS+QRQtVNRvNBSOEPCcQefGZ6HvSk5llv+ysTOUTb+QLtspOuEESP4Q0GwQ7HuW5qxSy3BdktXs6KjSdFYrsiZIPn2viQ5tNz5f9LLFSLe+JEVvi8JxswznN6qPS1Rib7ywXbF/ifjt/6WDd9XFM6wdDRoqnfLd8csNMx9m5T17/ylZvevPUGp3G7xp4gwYhW1ZWFS488aIiIZSIddv5Fc+eyxMoEcX63QPuhut7FG3SjPE2feg5Gq3z5sHELdkp5qjaL+qOK1r8HtXyKW5mhVb899a2HXYyqW3rr/Kc1NnzGxsIw/GTpbkJ65Sipvk9KkHsGne6/Wo3Q2wtZHFMs+aknKkNV9YwU0nlL4ki15pZLRVLk9+rnJ84oXWOqPKo690rfodbepXm0R2+sVx15NfL41il2/0ky+3ciuZpim85cskkkuugCZdJth5y9c6Ol6wAn+RehoUBx5qbcQzH27iRl/Fc2WVL/6Y/L11p8q7vpXL3wz7S5oOCGpg75IKCYtt9clgUgnrY8bcidIgdTG/wIQwVrwThsT8GUPG9Z/V9F0OpJF06QgrtPRgac17ecMs+6LHNjGxeznPiC/7P5kyBkvFssdjSo2NhlIj1TFQFzM3HiPZxTBxJttrOFIqFNjjMEXresKi41D/mQZh4k0Iq/e5U1WLdWKwy/LLsXnj7RKzPHCOrPfIoepfeX+R7FWTNqaqzR/+qfEx8YtM0y5XT6DljOWyu3RRxTl6+VsJnucpLM2nZKdpAkr0kaJ8V7LGXluf1jxSWm4gpKJ/pV/9RYCw4WuZu8APByU3afj+sAJ/iAQ7pamHfF1zE2V0iRFASgJJ/TF6PlWcvj9sqqdeZ9h6098iWKMrJhXfsbS0Rimcru0OQx2wNE/RdruWcW54xrlM73EMZDmXcufLLnuJ9aq2HijMfS+UIqYoyXIBDLpNsvZA9K/Nme85fQWGLecWNw7fwqx9oLd7dBeJ2EFMSqTE+pTm8XkzkTOAaKpmyB/Rj3yocfBdOTvVbukmfn4FUZCOTs9T6RohzGACTfC8dWWjELpF5ycLVlMvqTIgXzQMn6FpbZMLB4s0pQ9vmXk+VDaxhqug5di2t160ZdeVU5vlx3q6LmSqXTkpeEZenIMPE7wL5O9v9Us/5iEdM7ul5h8FGsUu3+tmP+QrPL3PaEIdWpe/7bEd7vaIv7yfRHfgSr2PwkrVGwWwYrPQEnPh6l3eq+ZdKsUeFVu1wTbrYguiQIef9hrrRwON1cqDr+gmHy7pbMJjr0Cc94mE8/pnTBheeKBZ7yrZ3IW3PwFCyZigNYNOx6F+e8iVp0bfUPJGbIjyh4rbzQ1B05vg92/0bz2VU12MbTViY/+tLvFVrq9znMz7Rm372yGLT/StJyBW//akJIr9xk9x7L9URFpG+eWCZBeaFnyYcm+ilYNR6/nT5LGMbkTvJDHmPlw6Dl7UUM8axRNp4iJfmejHNoPO6xi3+997Pv9UA/EcbVxgn+ZNFYoXvw7jS9ALBYdT9UOTdXO6OmiPB7uVlTvufB1m6s93xyFHBBH2fd7H6m5YfInex7+UWIi6IN5D1qsMcx/yHriTN9pkTYcacKuZJV/fHVU/aTTlLVQMN2zl7YWWs/I6jU1x7t31IMHZGzjlvfOpY8fY2pu5D1qEdSqXVB7SKptAZpOgw1bMT8r6J19Ex1L1S5orpLwS0qOd2BbNMe7745faEkr9cOhZ5V06YqOSffY0US8hpSCpLjfjlAXjFtumHW/JdwN2x/t2ypj039rJtwkNhEnN6hhF85xXN84wb8SrCLcfeHHL5XSm20sdm2M2AbEHxhufURTOBPyJxsmrJQVqi9Ar5j79Dd5Vb09Rb6jAcJdEn/vaJQY9Rv/3aCQ3UjFJs2SDxlGTZbnt9VLCqUvSWK+p7Yqwt2WeQ/2zpKJfp2cRWx3El9bAJIRY0Je8xNs5D2oyHYExaRbZffkQ7Jt2utld9BcLaZ00dfllsKMN4Wp3qtiDV6itRFRag8pXvxSdHZUpBdKrCnqsXN6qxzQ55ZK/+CDT2sC6bDoPZL+uu8JhS8Acx6Q0FAgFRZ/wPCnf+wd5gl1nf/w1+EYapzgDzO6WxQmbPHpSMy7refppFTx1hzwcWqzJTUPWmstcx+wjJomK/bKHVJoZPN657O31YkBXKhToQMWG7a88d897505D1jO7JeuTtHvZY6RTKTc8WLxUL5e4uNzHjAJqZrxE06wHQ48LSGitDyI9swFLz4f6pY5oLkaskoMi94n4r7tp5rWGiloivrq739SU3tIUbzAkF0sGUnR2H7OOJkot/1cUXqj7Ex6p0R6g2urUWz4nmb0XEPLmWgWVG+RfiWu1WXaKEt81o3/PDUBDsdwxgn+MOPYa4qccZbciVB3mJjve1+01iiSsyxz/kwE8PCLUgTUXqfIKBJr5pQsT4iD7bDm33XsMNMEFSVLTWKDEiWr+XA36FRv1V40CzZ8X9Nc6Y1nz+OKeZFzilCn54QJcPA5aD6tmPPWOMO0+OboiGBX75Vq4Kl3RkJDqbDgzw2rv6YJpBpyxsHpHTDtbsPC98jEE+wU7fUnkdAcPZAK237W9+FqIN2y6D1ie1C+UXH0ZU1zVf9SEdMLLLP/zMh9lYz94HNuFe8YeTjBv1ooObD1JVnO7lfn7aoU7lZs+Un/hCh7rGXpRw3+yCo7Z5wI37FXFa1npVn6kg+IMZn2iTVwtIAMIDnLMP8diSvzhnJJrdz035alH5EJAyScU7LY0Fzpja1yu6Z6t0X5LIWzLNPuklBOIAVu/AvY/XiikRv0PnQdPSfScapHBlK4W8UyY27+qzBZxfKc8TdIU5jOc5qxywxFsyOprhqaTp9fhOc8YMibLM+dfo+lZFGYTT/Q/agytaz4pCEpU4Q+1AVrvqHoaHCZLY6hpe2vX/a+eGxcv17jBH+QScmxpGTDhBWGMfMBKyGY179z+fnZGYWWjCJILzDoeKH0Q8F0y7FXI9+win1PKG77okUFYPRsWP6wYeMPxApizttsorOm8ap/m05LKmlyBrF2i219dO4qnGlZ+F4bK6yKWSsnSWPy6j0weq58r6MBUHLYGwsz9ajEtQb2/i7xPukFiRNCdgnUHpA0SqUk9HVyPbTXyZNSssU/v7kK2iLfS8v1/HqUkmvOfqthx/9eeHJVmpg/EEQaofdxSO9wXA0SRP4ycII/iBTNMSx6j2SaxPvcZxRBWp4cRCZimXiLJX+qpXq3onJb71Vk4UzL4vebWGPuaLp/tH9r9R6F8olFb2cTZI5RRPsWaz/kTZamJqe3yuFvz/h+bZl8o2SRjfnGWyMVqxV9NGBf8G6bYHyW4FZpper42Ksa7ZPdA8DEW8SczATh4DOKOW+X6mHtg+2PKmoOJr7vurLErJuKjYpR02wsOwhg0m1QtVMyaG76nHjfKB9s/qGm4YS0sMyZYGNj0/o8/kA9fyJGjO9GTZWvmyr7n2o58RZD6U2W1hrY9aur18PBce1wpQLfEyf4g8iMSKaMj4gPj43EnI347PdkwkrxdPcnw6gpYudQcyBRJHpmr5xYp0jJtPiSoWqHovEU3PFlgy9ZCn42/0jFKlSjB7gTb4H8SSahEToWms/Am74eprMJzhyIc+XUkdV5HzuSXhWvhlhVbzgMjRW9fVpOrFGcWON9XXdUmpy01Ullc0+2P6qZcoclq8RyYo2i6ZRGKYsOeKeoSkn189n9Cl9cbH/CjYaGEz7GzEtsvmKtfF79YfvPNaPnSGHVmb2K/lTd5k70fpYpOTK2i+0mHI6BFvieOMGPoiQMEOqGlqqBWYl1Not3v46ERJqrASsZJFFL4XhyS72uU74A5Iwz1BxIFInWGs+czVqoP6qoPeStiOc8ECaQLvfUWeKWuf1RxbKPxKWYRA44o2EKE4Lj62DiStkFpOZK9Wm4O5JNqaFik0YHLFljJE0zGMke2vNb7+C2uQpOrIHkbAm7VO3UnDt+8c8yfwpkFVu621WfZf7W9La3aKxQhNqlHiCK9olpmQmCTpbxR/3oo/18o2EnE4SqfprxWROtn+j/v4vUHC+rx+cXW2uHoyeDLfA9GXTBV0qdBFqAMBCy1i4Z7HteOtK3Nn8SoGUFWvbHKz+U2/1rOTRNzRMP/6N/uvA1q3ZKqqCOFAP1DG0AHHxW40815IyFU1sUtYcSRSgcRKp1teceWXtQU7UrzJh5kaYpBg79UWLsURsDn5+YQEVdFFd/XZM7wdJcpQi2w6ovmVgnqI3/pWk6LRW91Xuk0CjUxyQWSJO0zJazkhXUk/ErpJjJF4DJqyzrv6tpOdM/Ye1qFTO4KHt+K72FM4pg9FxL/TGvcG3fE5oVnzQkZ0ntwbafKbpbBy/EUntIEey0sQnT5eY74OoLfE+u1gp/lbW27ird65JJzYNRUzy/9UmrLGV/vPLrdjYqXv9O/7fxNQcUW36kyZlgqT+iErJOssdK1kwgVXz0d/1f35PH0Vc0o6YYskok7h5N69z9mKL1rCV9FJzarAkHwQSlMTkKihfICj07cth/6HlFZ6OiulFeP/n2cEKK55y3STpnSpakY4aDsPMXmtoyOdg0QakFWPEXciob6oR139S96gqKF9iEpu35U2y/BF8HxA8nOh4TgvZ6OYwu+6Pq9fNrq1X86Z98MWfPvkjKsBTOlJ4L9UevTKCDHYo1/67JmyQ7or4OvB3XPkMt8D1xIR3Efz2e4BD6n5w7rvoMgyx8j5ciOeV2S/Vu22f7vGC7Yt23o9688nj2OMsNH5dVdO1h8f1Jz/dCOtaK5035RphbInH4eQ9Z1n7DSuhGWSbeknifqJlZ9Bq+gFSfdjbLtVvOitD5k7xdRMli26tbWd0RRc74iFc99Lu5jQlKyCw58pkEO+S/i3E+sQ+kWW7962hXL8vhF+NsJi6TUJei5pBl/jsNY+aJn/6WR3QsHOa49hhuAt+TqyH4FnhJKWWBH1prfxT/oFLqYeBhgIK0oZl/gh2KHb/QzP4zQ6hbMiqGG/Hdnqw9f/cnD09U5jzgWTnnT4LCGeKDf+h5mPUWYq0S5z0Yd1DrgzHzLBUbFVnFkZh/XEZPvNjHjzF9lJf2GA565mTWiFNmT46+IvYUOeMtp7fpS+hmptj3e8X8d0ocavdv1BX51uSWepbRABNWWI6vvuzLxSheYBkzT66bPRZmvtmw5zfu8PZaYbgLfE+uhsKutNZWKaUKgZeVUoestWujD0YmgB8BTMlPHbKWEWf3K87uH76/iPufVCx8jxwE1h2WPPn+EvWYiV/RT1gZ8YiPbASUlvROE4q4RFroahYBDbaT4Isj5wIwel7ifRKM0pBexKZbQjtn9kHl9j4E2arL6lGstGXBuy2BVHlv899pefnLcYY9l0hbHbGahNgB+wAQP1FqP16DGceIZKQJfE8GXfCttVWRP2uUUk8Cy4C1F37VEKIsafkS1om2sxtMRs81TLzF0nImkr1znqKeM3s1f/onCX1IJkv/x7b3d5oVnzAE0qDmEHQ2WRZ/IGIPHGn5Z4JQuVMKlDKLoXKb2D6DpErue1Ix/Y3SLGX7o5rpb/R89sORXq4+v5fi2X4Ojr46eOELf0pi2mhSWuRAOnzh152PthrFzl9It6q2WunCNRBU7RI/oajthPOeH1mMdIHvyaAKvlIqHdDW2pbI3+8C/nkw73klKG1Z/jFDzgSR0+2PamoODp7oZxZbFvy5CG/OePAFDLt/ff5dRrBdsmUulZZqxUtf1hFBVORPtdKgBVl9drXIgat07Or7/Z7arDm12fvahBLDNbVlkYPvAHQ0w87/U5ct9knplkXvN2QWQcVmKHs+sUk8yK6j7ojnnFlzSN7blTAYu7xgu2L11zQZhTJRX41FhOPyudYEvieDvcIvAp5UshT0A7+y1r4wyPe8bPImiR9N1Alx1lsMNQcHL8yTUWhj1gK+gMR4Bw8VW/02HJcq37R8ydc/+IyiPtKQZcx8Q/FCy7njihPrzhcXF2fOqAZrDfuehNv/RsIW6Xmw5IOWVy5zap/9gCFvoqzYJ94soaHast7vZ+sjmoIZ3oQzXDEhRXPVUI/C0RfXusD3ZFAF31p7HJg/mPcYSMLdxETMGjHKGkzqjyps2MbuU7Hp6qz+TFjx+nc0OeOlv2l7vdw3f6pl/rtkx1EwXXYAfcXXoyGU2CEukJrlWThAnNf9BcgcbdH+6HmEd5+UbM8yQemINXFZ73FYI1bRDkd/ud4EvicuLTOOxgrFydfFeqCrBXY/Nrjx1u5WxZr/0BTNsrTVXXnu96Vgw4qGE4nfyxnn+eJ7vW77eK1RVO4QUzSsNClvrBDPm1HTZCJoroY7/jHMueOw6zHdq+hq+r1hJt4srz+7H3b+0ttJHXlJk/NhaT6ifTD9jZaaA7ZP2wWH40Jc7wLfEyf4PTj0nI9Dzw3gBZWlYLr8tbaMXiGSrmZ11Vb2F6O2TDH1Llmlm5A0Aj8fux7TjNoqmS0STlFs+5llzHzLvAfFpkIp6V875Q2Wwy/Ep/BYJt/mreJHz4XkTBuzKq47rKg9AqNnAUrSPYsX2IR2jw7H+XAif36c4A8yi99nYoJfdxS2/XT4pH4mpUtRUHoBHF8trQ03fE9TMMPSdEpRdzgqsGIENn6Fpa0Otv9MfOTrjvS8omLqXSYhnKP9EV+ZeKxU3sZSFG3v8FlrNYSnRjyDwtDeh8eOwwFO4C8FJ/iDiC/JUjTHW8kWzgRfsu3TOG0omPeQTEbaD7P+zNJ4ytJcqRK6WoGYm028RVJCA6kw9x3mvBNXtHAJvJz9E+t6txvc8hPNwndL2Gbv73unox5+SZOSbcgtlUbl1buGx2fmGFqcuF8ZTvAHkXAwcSUb7uLCTc+vMumjIkVWyCF1Wh40V/Z+XlKG5/yofcQsHvpi/1OKRe+V5zdXi0lZtIArnsZyxWtflUlDaUtKtqWrhYT2i9GOV47rFyfwA4sT/MHEKjb9j2bu2yT3ct8Tl9/l6nyk5lpm3CvXL3te036u/9c/+qpi7tslNTTYIRW8fVFzUNHZYklGsmbKXjj/YfbZfVIgFkiD9jq4WIFYSrZl5WcNSalyUP76d3obrDmuL5zIDx5O8AeZ5krF+v8crJWq5cZPeaZq+ZMNf/rn/k8qlds0zZWW1FzJde/L3hgg3KVY+x+arBLobITOpgtf/1IKxCatMiRnRHYO2TDhRsuRl53gXy84cb+6OMEfwfiSEvutJmVI0dil1A+0VCta+uEbY0KKxvLLG+eFr0uCT8/lWiM4Rg5O5IcOJ/gjmHC3orFCzMkAWqoGv1hsoDn2qqZgmvj3N1XCydfd6v5awwn88MEJ/ghn0/9oxi6WJfLp7f3rtzqcCLYr1n3LB8oO+PmGY2hwAj98cYI/wjHB4VO4dUU4sR+xOIEfOTjBd/TCn2KZeKtF+ywn1upB7f3qGHk4gR+5OMF39GLFJw0Zo8UaoWSh4dV/G/h00tnBuk8AACAASURBVMshkCYppKHOoR/L9YQT+GsHJ/iOBNJGyQFq1AkzOQuSMyRHfiiZdo9hyu0WCxx4WlH+umskMlg4gb92cYLvSGDBuzzfG2ulD21X6xAOCAikWqbcbmNVwbPvt5Svd4e8A4UT+OsHJ/iOBJIzvdW9CcOBJ6+sOfhAYEzi19b2/TxH/3ACf/3iBN+RQNkfFfMfshgj1ghn9w/9Kjrcpdj3hGL2AxYM7PzV0E9CIwkn8I4oTvAdCVTt1DSctCRnQdMpz8xsqKnYpKnYHDVxGx5jGq44gXecDyf4jl50NCg6hqP/vFvV94kTeEd/cYLvcIwwnMA7Lhcn+A7HMMcJvGOgcILvcAwznMA7Bgsn+A7HEOME3nG1cILvcFxlnMA7hgon+A7HIOME3jFccILvcAwCTuQdwxEn+A7HAOAE3jEScILvcFwiTtwdIxUn+A7HRXAC77hWcILvcPTACbzjWsUJvuO6xwm843rBCb7jusSJvON6ZNAFXyl1D/BdwAf8xFr7tcG+p8PREyfwDscgC75Sygf8F3AncBrYqpR62lp7YDDv63A4gXc4ejPYK/xlwFFr7XEApdSvgbcATvAdA4oTeIfj4gy24JcAp+K+Pg0sj3+CUuph4GGAgjR3pODoH07gHY5LZ7AVtq8WRQktqK21PwJ+BDAlP9W1p3b0wom7wzEwDLbgnwbGxX09Fqga5Hs6rgGcyDscA89gC/5WYKpSaiJQCbwTePcg39MxAnEC73AMPoMq+NbakFLqL4EXkbTMn1pr9w/mPR0jAyfwDsfVZ9BPSa21zwPPD/Z9HMMbJ/D9x1pL+at7OHe0mgm3zSV/eslQD8lxjeDSYhyDwrUs8A1Hq+k410rRgon4kgb+V+jgr9ex5bvPYIIh9v78Fd7yqy+QM7FowO9zMay1lD25idOvH2DsTbOY/tYbUKqvPAzHSMEJvmNAuJYFPp4Dv17H1u89g9aazHGjuO/Rz+ILDOyv0f7H12GCIQDC3SGO/XE7iz/5pgG9R384/sIOtnzzKUKd3VRtPkwgLZnJ9yy66uNwDBxO8B2XxfUi8D3Z/dOXCXcGCQPNp+qo3VfB6IWTBvYm4cTs5FBn92Vdpru1k9PrD5Cal8mYpVMv+fU1e07G7h3q7KZmzwkn+CMcJ/iOfnG9CnxP0oty6DjXCtZiw4a0UVkDfo8p9y9j949fwoTC6ICfCavmXfI1Qp3d/OHPv0FHfQsAc96zikUfv+eSrjFh1VwOP70ZEwyjAz4m3Db3ksfhGF44wXf0yfUg8F1Nbex/bC0As991C8nZ6Rd9zaqvvZ/Vf/sLOupbWPixu8kaN2rAx7XgQ3fgTw5Qu7ecyW9afFk7iLqDp+lsaCXUISv0Q79bf8mCX7xsGvf84BOc2XGM0YsmUzR/4iWP41KJnhuc3XmciXfMZ/ytcwb9ntcTTvAdwPUh8PFYa3n2w9+j5VQtACde3sUDv/viRQ8lM0vyue/nnx3UsSmtmfveVVd0jYzRuZiQkev5NNkTCi7rOkXzJ14VoY9y6Lfr2frdZwh1dnPy1d3c+e2PUrzs0sNRjr5xgn+dcr0JfE9C7V00V9RiwyKKzafqCLZ1kZSRMsQjGxgyxuRy+9c/wM4fvkBaYQ43/s3bB+U+h36/gcN/2EzB7PEs/ez9+JMD/Xpd29lGVn/pf2mtbmDeB97AzAdvAqBq65HYuYHpDlG776QT/AHECf51wvUu8D3xpyWTWZJPS1U9AJnFeQTSk4d4VOen4Vg1m7/5FFhY/oU/I3fymIu+ZtxNsxh306wBH0trdQO7f/YyHfWtVG48RLgrSMPRanTAz/LPv6Vf11jzd7+kZs9JrLFs+e7TFC2cRN7UYiasmsvpDQcJdwbRAf9lHTY7zo8T/GsUJ/AXRinFm3/6afb+72sAzHnfqmGbY26N4fmH/4uupjYAnn/4v3j3y/+M0vqqj8WEwjz7we/QUd8iLohWMorCXUHOHT7d7+u01TRijbxWa017bTN5U4uZ8qYlJGWkULuvgrErZ1I4t3Tg38R1jBP8a4hrTeQ76luo3VdOzqTRg3I4mpKbwdLP3Dfg1x1oQp1Buls6Yj6z3S0dhDq6CaRf/fBTZ2MbnU3tMbEG8KVIGGfG21f2+zoLPnIXG776O7RPk1aUw+hF3sH0+FvmMP4WOaztampjz6OvEu4OMfe9q0gvyhmgd3J94gR/BHOtCXw8LVXn+MO7v4E1Bhs23PmfDzNm8ZQhHVNnQyvnjlSTO2U0qXmZV+2+gbRkipdO5ezuEwAUziu9oNhXbTnCuSOVjL1x5hVX6Ia7Qxx7YTs2bJl8zyJS8zLIGJNLa9U5UIrcSaOZ9dDN5EweTcHs8f2+7tT7llE4t5S2miYK55eeN/b/x0/8N43HzmCt5eSfdvHgM19GB3xX9J6uZ5zgjxCuZXHvi5N/2kWooxsTCgNw4LG1Qyr4TRW1PPPeb8XCGG/+6WfImTyaw3/YTOWmMsbfPIsp9y4dtPvf+Z2PUr5mL1gumA9/9LmtbPi332HCYXb89x+5/xefvyLRf+lTP6R2XzkAZU9s4L7//Rz3/fyzlD2xER3wMf2BFQRSL+/sI7u0kOzSwvM+bo3h3OHK2M6mq7mDjnMtl7XKt9Zyev1Bgu1djL9lNv6UpMsa80jHCf4w5XoT+J5kjMlDB3yYUBhfkp+s8ZeXVjhQHPnDZrrbOkV8FBx4fB1F8yey+T+eJNTZzel1+/GnJlN6+6UXSZ2Ppopajjy9hfSiHKa/9QYm3rHgvM+11hJs7eTIs9u8ylylqNxUdtmCH+4OUb3taOzruoOn6GxoJTUvk6SsVI48vYW26gaWfPo+fEl+Gk+cpXJTGfnTSxi9aPJl3TMepTUFcyZQf+g01lpS8zNJzb+8ndX6r/yW4y9sByBrfAH3/+LzaN/VPwMZapzgDxOud4HvSekd8zl3uJLjL+2kcF4pCx++e0jHk1aUgy8pQLgriC/JT0ZRLmd3nYizHghSs/vEgAl+R0Mr/5+98w6Motza+G9mtmTTe4MkhITeIfSONAEFFMWC8l17vzbUa/dar717Va5dFLDQO0jvEEILhCSE9N7Ltpn5/phkkiUJRcW6z1/s7Mw778yS8573nOc8Z8l1r+OosSKZjJQkZzHsyauoK6vm6LxNCJJIt2tGIhokqrKL2fTkPMrT8zF4mJDMBmSbE1EUf5HSpmiUkMzaMwOgQmHSSQyeZna/thin1U5pSi6iyUCHSwaw5LrXUZwyilNBMhno+Y+L6HPz2X+3nB3HqMgqJnp4N7zC/dn9+mLSVu4jsGMko1+aTdrKfch2J12uHIZo+HnhnNTle1Dsmj5R5akiqrKKz7i7+KvCbfB/R7iNfOsQBIF+d06m352Tf++pANB5+mCKj2aSs/0Y4f3i6X7daHJ3p5C6Yi+yzYlkNpyRAik7nBz6fAOVmUV0njGU0J7tzni/0pQc7R+qxoDJ3n4MVVFYNvtNqvPLEASB9FX7qSupQrY79dCXo85GUMc2eAR4E39JfxdPW7Y7KTyUgWeIH371OyZVVakrqcLoaWb7CwtJX5OIT2QgE96/HZ/IQAI6RFB8OBPQFoCsLUfxiQpGVbT6BdnmoORYNpYgH83YO2T9+KHPNtB2SJczxvYPz9vE/vdXoMoK+99bTv97p3L8xx046+zk70sj8aPVDH/yqjP/OOcAn8hAKk4VaawigZ+9U/izw23wf0O4DfyfF6JRYsTTrs3aooZ1ZfybN1Nw4CThCfG6BEJtcSWCILgYlR3/+Z60FfuQbQ4y1h9k2vw5+LZtnXkUEBehM2Ekk4HwfnHYKmo1OqOsoKIVi50OQRAI7hrF0Meu1I8pDpkt//6G9NWJ2jmSyLDHr6T9xH6su/djcvek0sBIVWWFyqxitj2/gInv3caAe6ey5u4PURwyilMmddU+TN4WzdMWRQRUOl02GLOvF4IkQr3B116aoFNJW8OJJbt1+QfBIFF48KT+3IpTpraw4ozXnyvGv3MrO178Dnt1HQn3XILJx/KrjPtng9vgX0C4DfxfHxH9O7gUB+3/70oOfr4BVJXeN42n903jAcjfl6aHRgRJoDQl94wG3zPYlymf3EPygq3UllSSuyuF5Te/g0eAN3UlVQiCgGQ24Kizg6KCIIAAXqF+9L55vMtYx37cwcm1B/SqYlVWSPxoNZZgX/IPpOtSzE2Rvy8VZ52d8D7tmbniKb6b9jy2iloUmxPZ4GDI41ci19kJiI8gpHsMAEMfvYJDX26kPD0f0WjALyaEiIQzF06FdIum8lQhst2JqijETU4ge/sxnAYJVVbodcNYl/NVVaUmvxzZ7mDbCwupySuj5w1j6TRt0Bnv4xMZyPh3bjnjOX8HuA3+rwi3gf9rQHY4cVodmM/TC3TU2Uj6ZJ1uWBM/Wk2P68cgmQzEjOpO8oKtOG2acQ3pfnYKY2CHSHpcP4YfZ/4H2ebEWlaNYBDpcOkALIHetBvbm58e+ZzqnFLaje1F71smsPM/37Py1vfpMXs0giiiOhWqs0v0kE8DPEP8NB1/teV7C5JI2cl8grtEYfb1JLBTWwr2p6E4ZVRZJqxXLN7hAS7XxE/uT/zk/tQUllNXUkVgh8izxtwHzZmOwcNI+upEbFW17HljCZP/dze1RRX4tg3GM8RPP1dxyiyZ/QalKbn1BV8CqCo7X/mB0B4x51R9/HNRmVXE6rs+pKaggk7TBzHoocv+sIV6Z4Lb4P8CuA38Xw/5iWmsufsjFIeT6FE9GP3i9edc0SpKEoIooMoNn0UEUTMKnaYPpiBJ05cfNOcyvELPjVp4ekhEdSqUJGcz9esHAJjxw6P6dytve5/8/WmossK25xYimSRAwKdNEEZPM4pDRnY4CYiPYORzs/AK86f9+D6kLN2N2ccTk49Fk5pQVFRFYfmN7yCIAiOevpoxL13PzlcXUVNQTu+bxjUz9k3hFep/zs9n8DAR1CWKlEW7UJ0KpSdySfpkXYtx+6PfbKb0WE7TtwHUV+oWVlxQg7/12flU5ZSCqnJi6W5iRvf8U2r8uA3+OcJt3P+aUBwyFacK8Qz1w+zryfbnF+ox5extyVp8/hwphpLJwPCnr2bbcwtAEBj+1FUIksiReZvY8/ZSFIeMIIls/fe3zPjx0bMPCAR1icI3OoSyE3n6MWt5dYvnVuWU6LsLVBW5fjdRmVXM1HkPYi2pxD9OKxqT7Vr7RGt5DW0HdyJvb5rGOFJUPIK8sZXXosrayrXxsa+4+OO76DxjCNueX8D2l75jyCNX/GoGz1FrQ62XaFBlBXtlXYvnlablNTtm9DRjCfElrPev3ITm9DnW2HQZCQQBZ53tgt7vQsFt8M8At5H/a8NRa2PJda9TU1AOwIT3btMSj03Q4KGfK+Im9iNuYj/984mlu9n77nKdvaIlRYu05ibnQDEUJZFLPr+PJde9TlV2Caqi0ve2i1s8t+fsMex8fRGqQ26UPhAETN5m/KKCCWgfhq2yltV3/pf8/WnIDmeLIR1rieuCosoKK2542+XYuvvncs36585ZHfNMiJvYlyNfbaSutApBEulza8tUzvYT+pK2Yp++qHW+YijRI7oT3qc9BsuFLaQacO+lrL1vLqqqEtA+nDaDO1/Q+10ouA1+E7gN/N8LGRsOUlNQrnv0+95fwdDHZ7Lm7g9x1FhpN7Y3ob9QC77wYEYjjx0tNh7as9158ckNZiM9Z49h67PzEUSRI99sxhLsR2RCvIvMQOcZQ8ndfYJTGw8BKogCwV2iGPnva/Xzdr2+mLy9qc1i+ucLxSnjrLVhMBvJT0xnw5xPcdTa6HfHJLrPGnXGa+3VVpI+WYu9uo7us0bjFx3CZd8/QlV2CV6hfq3KRrQd3JmLXvkHGT8dJKJfPPFT+v9mcfSI/h2YufJprGXV+LYN+l2E634N/K0NvtvA/73RVPtekETMvp6E9ojh2p+eR3FoFb6/FMXJWS6fO88YSuz43hQkpbPr1UVU5ZQQ0qMdseN6Ezexb6sLwb4PVtbvEmRKj+ew/oH/Edgxksn/u8elYlR2OBvDOoqKo86GtaKG5WOfwGlz4BXid87GXjCICKA3UtEOChg8jLQZ3BmPAG8ANjz8GdYybVew560lBHdtS3jf1mUw1t43l6JDGShOmYy1SVy54kmMFrNLRXBVbinWsmqCOrVxeSfRI7v/bl2wzD6W807k/9HwtzL4bgPvRlNEj+hG+4l9SVu5D7/oEAbNmQ5oXPazGfvKrGIyNiThGxVCzOgeLXqaqqpS0jTJKAlkbEgief4Wl/Oytx4lb3cKmZsPc9HL/2g2juxwaoyapsfqNejLTuQS1LmtfrzXP8aStfmI/rkis4iVt76nh5QqThUimgxaT15FxT8+gor0fE3CwmjAu00Q1fllKDYHXa8agcnbgyNfb8JeXYfJx8LA+6fh0zbIpQuWtbSq8ZkVlVV3fsj0b+fgGx3Cvg9WkLMtmehRPelTTxctPpLZWKDllKnOKSUgPoKCpJNU55Vhr6pl9xtLECSRwPgIJn10l1sw7VfCX9rguw28G2eCIIoMe3wmwx6feV7X1RSWs/ja13Da7IiiiGeoH6E92jHggWlY6r1ep81B7q7jeEf4U1NQgaqoSEYDdUWVLY4p251kbTrS7HjxsSzW/nMu1vLmBUyqouIR6O1yLLRnOwyeZpy19UlFp4Jy2nXtLupJ+toDICuUHc/ROPyqNgdrSRUT3r0VR7WVNgM7IRol+tw8AafVjmQ2NlvYFKfcLA+gOmWytyVT/f12jny9CUBb+FSVPrdMIKJ/B3J2JKPKKorDidHLzNFvNrP33eUgaO+O+hxEaWoehYczCO/zy7V53PiLGXy3gXfjt0DBgZOah+xUkFGoyi6hOr+Myuxi2o/vQ0VmIbm7TlCTX4aqqvjHhRPQPpyq3FKKDma0Oq53hCvVsSw1j2X/eFvXgNEhgNnXiyH/mtEi/dE7IoDytHxAqxBWmlS/CqJAXUkVNA3TNLBPRAGTr4WVt76Hqqh4hfpxxZLHESWpVXVJ0SDhEeTtkugVDBKKopCyaJfLuRkbkuhzywR63zye3J3HUdGSy9tf+p6KU4Uuom/61GQFD3/XRc2Nn48/tcF3G3g3fi2UHMvmp0c+x15jpf8/L6XDlNaljgM7RKIorn6z6lQoOZZNaUquS5IWoCK9gOnfzGHBlH+3OqYgigx66DKXY9nbkxvj8U1gMJvwCPBi46NfcPDz9Ux87zYMFjM7XvqO/MR0zAFeiGYDis2JIAiIBkmP26sCmP1aj0NX5Zbq3nVNfjkHP1tP+/F9yNh4mBOLdxHYIYJhj890SaxO/eoBVtz2PtW5pZg8zdgqa9n71lKXJimATm+1llYhmQz1RVwKlZlFBLQPoyavTGMvGSW8wvyxV9XR+6Zxv1jT341G/KkMvtvAu3GhsP7BT6jOKwNg+/MLaDOwo0uVZ1P4x4Yx9vUb2fHS91RmFunHBYOIXOdodr7ilPl+xksYPM26kuXpiJucQGjvWMpPFuDTJgjJZCCwQySCJLoafQF82gZRlp4HCpQkZ7P7jSV4RQSQtmo/ss2BkF2M0duDkL5xdJ4xlI2PfgENt5RVMtYebPklKCqiyeCyo0j63zqS5q5Frj9WlV2MwWJ2KYxKXb6XuoIKVIeMraIWQOfV69MWBfrertFJw/vGY/LVFh1FUehx/WjajenJthe/oyqrmB6zx9B+fJ+W5/gHgNNqRxDFXyWp/1vjDz1jt4F349dEyuJdZG4+TJuBneh8xVCXeLStslb/tyAK2KutLRr8upIqrRpVEDBYGjnoolEiID6S0pQclBYMesXJAkBr+lGRUejy3eRP78HD14sFk/+N4pAx+3ly6VcP0GZwZzpNH0zywq261x3asx2hPdpRltpYhJS2ah/ekUH6zkJVVOyVdeTvT2fo4zMZ/sw1bH12Ps6asxcLBXVqqzU8adKrtikUh0xFhvYstqo6bOXV5Ow83hiOaQWCKFJ6PJeIhHjqSqsY9tRV2Kus+EQGEtwlCoAxL80+6/x+byR9uo79/12JIAgMfXymvhOsK9X0jRqYS39U/KEMvhLWgZo5K37vabjxO6Eqt5SfHvqMmsJyevzfRXS/ZuSvNnbGhoPsfPl7nFYHuTtTkEwGOjYR3Op+7SiSPl2PIAmE94tvUSs9Y0MSGx/7CsXuRBAFBFFEMGh6NYpDpuRIJpLZSPtL+hPZvwPHfthBbWGF1g6wHqcb+y5XDCWsZyybn5qHvcoKqorikDmxZBc9Z1/EwPumUpaWR2HSSUSTgV43jEU0GDj81UZ9DMUhU5lVxOlQHE7KUnNpO6gzsWN7c2LxrmbnNIXBw0TnGYMZNGcaa+75GHtVncvuQjRICAaR7rNGkbs7hXX3zUUFLIE+jbr5glAvL+EailKcMpue+Ir4SQkc+WazxsDpEMmkj+4845z+SLBV1pL44SpUp6ZWuu35BcRPTiDxw1Uc/Gw9AH3vmETP68cAmnOw5p8fUX6ygNiLejHsqat/96YrfyiD78bfG5se/5LiY9mgqux7bzmR/TsQ2CGyxXOLjmRSV1xJxIAOzVrsqarKrld+JGXpbrxC/bj4gzsoOnwKp1XzVp1WOwVJGbrBz9iQxMHPNyCIAn4xoVz06j9apFnueWupHu5QFRVV0aplG4IXqqLitDqQbU5dSKz0RC6LrnqlcZCGyl1FRTRKRI/SOOUmbw9ESURxavILRk8tRi4aJS7+7x2kLd/LthcWsGHOZ4T1jQMBV3ZM/XiKU9G9c1VRWf/Ap6iq2swAm3wtOGpsqLKCaJTwjgik720TiR3fh9w9J5BtDpdrQnu1o8uVwwiMjyQgPoIfr3pZf5/W8hq6XjUcBIGIfvFsfPxLHNXWZvesLazg4Ofr9XmXpuSQvz+NvL2pyA4n3a8Z2WoY7Y8IAa2I7OCn6/Ucyb53l9P96pGIRondby6hNCUXVVbI2HCQtsO6/u6hqgtm8AVBeBq4GWhwPR5VVdXtvrvRKuqKq3RjJYoidU343U1x+OuN7H9/BYginsG+TPvmQSSzkeM/7KAw6SSeoX4cree6V2QUsnjWa4z+z2yOfrtFTwq2G9tLH2/Pm0v10EVlVhGFB08RkdC8cOh0DXXBIGpSDE0KmQQBl9huYIdI4qf0J32NpkWvOGU9PIMKR77eRHl6ASmLd6GqKqJBInJAB0J6xPDtxc9QV1JJeL84ytPy9dh/QWI6otE11o4oaGPXUyyRRFDUFousBFHgqhVPU5ldzLHvtuEdHkC3WaOQjAZUVeXIVxv16mNEgYi+cQx8cDq7XlsEAgx6cLq2INUvOrLdwaH6BVNxyqj1yVgAyWJ0zWs0WaRURWXbcwuoztdyJydXJ2qsoNOKz1RFIX9/OoIkEtY79ryqa7O2HCFttdY1rctpYbzzhdnXk763X8y+91foIR3JIGnvoR6iJOqLuq2iplGSWlWxV7WsEfRb4kJ7+G+oqvrqBb6HG38R9LltItueW4Agifi0DWqVe334q426d1lXXEnRoVOUpuax793lWixZcv2jriupIqx3ey7+8E7y9p4grHesy9hNDbmqqK02xxj57CzW3Psx1XmlSEYD4X3jaD++D9teWIDi0Dxrn7bBJNzl2qVr+NNXEzu2F0mfrKOwCS1Tccpkbz9G9vZj+jFzgDfj3ryZxbNeo7ZQ0/jJ232i2Vw8Q3ypK6lGtto1g6MvIipeEQF0vnwIiR+ucqFkNqDd2F4YLCYCO0Qy5F9XuHxXlppH/r40/bMoiox4dhaLrnpZS8gKsOKW95j88V2svfdjagorGnWCFG2xkDy03IZokAjtEYvJy0zOzuMA+LULQ7Y7sFXUEto7llPrkvR7WcuqtSblp1FNNzz8OTk7jum/jSXIh/53Tzmrnk1+YjobHvkc2eog86dD1OSVEtS5LWG92/+sRugAPWdfRNerRiCIgl4MN/TxmWx/YQGCIDL8mcawTd/bJlKQmI6KiiXQh9g/QCLaHdJx4w+D+EkJhPZsR11xJcHdoptVlzbAp00QdSVVqLKCIit4hvlzeN6mxsThaXRA3+gQBEEgtEcMoT1imo038rlZrL1vLnUlVfS4bnSrfWD9Y8MYPOcyNjz0GYpDxq9dGB0uGUD0iG7Ya2x4hvppHl89qupj9z6RgUQN70bqir3QCkGmAQ0qjLqH3QSS2YDiVOh29Qh63zSe5Te/S0lyVrPCp7qSKsJ6xTLg/qnsfm0xiILmdSsqgiTiqG09wWrwMLkwbCzBvhg9zdirrdoBFeyVdXhFBHDFkicoOnKKpde/6TJGx2mDKDuRi1eoPwMfnI7Jx0LmpsOoskL0qO7673o6TdXo5YEl0LX1oK2ihqzNR/SdSp3NQV1xJese+IRJH99Jzs7j1JVU0eWKYS70TXu1lczNh/XFyGm1c/irjVo9gQBTv34A36iQVt/DmdBUMM5ptRPWO5ZZm17UchxNdhDBXaO5csVT1BaU4xsT0ur/598SF3oGdwmCcD2wF3hAVdWyC3w/N/7k8G0bfMZOUACjX7yeLU9/Q3VBOX1umYBfdAgxo3qQtzsFp9WBZDYy/MmrSFu1H0uQL/3vmXLG8fxjw5j29QMkf7cNxSFjLa/Bw9+L2uJKyk7kEtixjd6ucMsz3+rhn+Pfb6fLjCH4xYRi9vNyGXPvO0s5/PUmVEUlIiGOkc9fT787JpGz83ir8r+CJOIfH8F301+gKq/U5TvJw8igB6fTcdogBEFjEdWWtNz+T7E7WXPPR1y99t90mTGUoiOZrL5TE4RTZYXCpJOtvgvfqGB63zSOxI/WYPQ00/vmcSBCREK8vjsJ69Nez5sEdY7Cw9/LpRI45cedXPrV/WRtOsyet5fS+fIhenN32eHEUWfDaDHjGx2ihXPqe5kMuH+qlhNRFMrS8jH7euIR6F2fm3Ddqcg2h7bQCFoTsVcedwAAIABJREFUlNRle7liyeN4+HtReOgUq25/vz7PooVUBFFAVVQctTYESWT3m0voOHUgUcO7/ewwT0VGIctueAvZ5sAS7MulX96P2dfT5Zw/mv6OcDpf9rwuFoR1QHgLXz0G7ASK0X7OZ4EIVVVvaGGMW4BbAILD2/R7e8XOnz0fN/7eOLXxEMVHMoka3u2sTcJPx9LZb1KSkgOKile4P2NeuYEVN72tG5RLPr8P/9gw5o17UteOkcxGpn3zIH4xroweZ52dL0f+yyVp6Rniy4wfH6PgYDqr7/iw+QQENEmE06mTooBvVDDRI7vT/+4pCKJI0eFTrLr9Axx1tlY7VokGiSuWPK4VMFVbmT/paRw1mrGLGdWDXjeN48jXm/AM8aXXjeMwWsxkbj5Mxk+HKDqYQUVmESgqBosJQRTxjQnGOzyA2HF9aDemp0ucvSQlh6XXv6F70wZPM5EDOpCz4ziyzYHBYmL6gocpTs5i46NfoMoKnWcMpc8tE1hxy7tUZBQBKgaLmanzHmTHiwspTMpAVRWGPHolPm0C2f7CQqyl1Tjq7Mh2R/PnFrXcRWCHCCoyCvW6AdFooM2gjkhmI1lbjuqLtWiQEI0S3a4dSb/bJ53lf0fL2PT4V6St2g+qimg0kHD3ZLpfO+pnjfVLcU3fqH2qqiac7bxf5OGrqjr27GeBIAgfA8taGeMj4COA9l17/vzVx42/PWJG9SBmVI/zuiZjQxLbnlugFwyBxiY5+u1mrelFPY7/uJNO0wfRadpADn+1EUVW6Fzv3Z8O0SAhSiJyE4Nvr7GRtzeVjY992ZxhAwiShGxtXrSFqlKdV8bRb7aAAPl7UqnMKsZR25xTLxhFVId2T8Upc3TBVvrfPYWq3BLkBg9ZALO/J8tvfAdnrQ3RZKAsLZ8uVwzjp3990WwODaGlkqPZlKcXENwl2sXY15VUseLmd3UPvEHwTEsy1/fwFQUKk06y6Ymv9Oc+tnAb8ZMSkEzGRlaRUyZtxV4KD2bo4bk9by0heng3DBYz/e+/CO/wADY/8bXew0BHg/bOibxGqQi0hG/cpARiRvVg16s/kr39GLXFFY1N2Zft+dkG32AxIUgCqlNFkIRW5Sf+SLhgpFBBEJr2G5sOHL5Q93LDjZ8Dp9XOpse+cjH2iAJmP0/8okOQ6mO1ktmA02pj8azXOPrtFkSTgenzH2bg/dNaHFc0Sgy4f6rLMdnmoLa4QjNG9fbII9AHQ32CU5CElpt4qFqIRnE4Ofz5TxQfzWqV7dFg7Btw+IsNKLIm+SDW67erToWcnSm6gVbsTgoPZmgNUVpacJo+g9XBwS82aN276hezvL0ntOvqn8kS6M2kj+8iemR37dm0DZIWojptkctPTCO0R7vG8e1O8venueQvnHV20lbuo/hIJjteWIhkMnLRaze03vBEVV1YM77RIbS7qBeSycCQR6/g4g/v0JOqotHQar6mJdQWVZC5+TDV9eG2vrdfTED7cARRJLxvHB0uGXDOY/1euJAx/JcFQeiN9jNnALdewHu54cZ5Q2naGQpAEOh82WB63TAOk58nR+dvobawAtkhU3w0C9nqQEYzFDk7j+Ef29y7b4BXmD+SxYRcb7wMFhNeof66oRQNEpYgH9pOSaCmqJK4iX0JiAsn8eM1VOeU4hUZQOqS3ef1PM1kGEQRQYCwnrGoqoogCogGA7WF5Xr4RTCIRA3rSuSAjhyet9GlSrgh7NEQHlFlBUdVHUfnb8ES6INPVBAbH/3SZQ61xZUsuORZRj4/C//24VRmFxM/KYHCQxl6HL0BYb3bE9ChjpTFO/X55O9NdRlPVRT9/k6rg+M/bGf4U1cz4P5L2f78d/pzm/29cNbYkDwMeIUFUJqSg1eYPxPfu82l2MmnTRBj37iJg5+tx6dNEP3/eek5vduKzCKWzHpdn9PED+4gtEcM076Zc07X/1FwwQy+qqrXXaix3fjzw1lnR5EVlyYkFwpl6flseWoe9morA+6bSvSIboBGx+x0+RBSFml5o+6zRtHvDm17n5+Ypjf1QFEpPZGHZDIg252IBhGfNoEu96jMLqamoJyQbtEYPEx4hvjpxh7AUW1lzT0fgQBGbw+cdXbKTuRSlVXM1HkP6KGh4U9ehSIrzJ/0TMsPIwoIQvNKVoCIAR2QjAZND18UGf701ex5ZxlHvtqEwWIkbuogJKPEiaW7dQPrFeLHsCdmIkgiQR0iNRljUaDTZYMZ9OB0BEGgPKOAHS99T94ejR4qWx0UJJ1kz1tLms9P1UJiK29+j2nz59Bx6kBAS8afXHuAnB3HkIwGEu6Zgk+bINJW7NWTpoIkaknWJmuwT9tgXfkTIHXlPgbcP439H6xufCVGiXGv34TZ3xPPED/W3vsxktmItayGtffOJeGeKViCfAjqqHnzkQM6EjmgY8vvtxWkr9qn5UzqF6xj321rkfH1R8fvzxNy42+H1BV72frsfFBUus8aScLdl1zQ+62992Oqc7Rt+E+PfM7MFU/h4a+xagY/dBldrxqOIAqnsYMEFw676pSJGNqFqpwS4iYnENw1mpW3v09VVjHh/eM5ufoAoiRiCfZl6tcPkL0tWUsknkYRRT29ITYUJJ3UDb7T5mDFTe9QV+yqmy8aJXzaBNFx+mDSlu+lNCWH05G74zii2YDRy4wgSVgCvElesBVVUXDU2Mjbk8KYl/9ByhJNYkEyG4kZ1QPRIFGdX0ZpSq4e6jm2cBuDHpyOIivseXMpBYnp2jxMBkRRoPBgRjM1zNOx8+UfdekE0Sgx4Z1bqcotYe87y8jZmcL+D1ej1r9j/7hwfKNDyN6W3FhQJqD/bo2/iiYZYfQ0NzZeUbXKYd+2wcgOJ3l7UvX3W5qSw4Y5WrVxwl2T6Xb1z5Pr8A4PxGAy6CywszHJ/qhwG3w3fnNsf2Gh/kd9eN5mul41osWSeq1jVDYAQZ3b/mz6XF1xY8WuIICtnnYJWtw4r15KIP6SATqFrrboNMqjIND75vF6zHnNPR+Rvy8NVVZIXbpHqzgF1OJKcnYexyvUX9sRtJKIFYyS1mxcVfGPDaOupApLkA85249RfprejtHLg2vWP0tZah4rb30P2SGDAKLZiHLa+IrNqYVlBK0totAkoC3bHPhGBTPq+evY9sJCbBU1FB/PwV5txeRtcdWhV1UWXfMqtUWV2Moate7Nvp5MfP82fpz5CmdDwYF0rGXVLoJiK295j+qCcpdcRgPGvnoDKUt2k7JoJ6UpOTjr7JoyZX31qiAIdJ4xFEugD6NfvI61987FVlVH9+tG4RcdQumJXFKX78Xsa9HE8OrHb8gJHPx0/c82+PFTEihNzSVz42HC+8XRY/aYnzXO+UJVVayl1Zh8Lb8Kj99t8N34zdGsAXQrhnz7CwtJW7EPgNgJfVwkec8VtUUVeIX7U5lVjGQyENwtGt/oRu9s7X1zKTiQDopK8nfbuGzBw4gGreFHQwgHtGRkSPfGLXx1XpkeVhEEQbMtqgqKimeILyGjulOcnEX66v0uxke7QGuK7RXki2AQWXHzu4AW9jAHeKE4XdU2ZZsDW1Ude99Z5sIcUh3NVTkbv4SSY1kEtA+n/GQBqqxQV1rNvIseJ25SgqZ141QoOpRB0v/W0v+fl5Bw12RNPgFAUSlLyW02rCXQm4C4CII6tdEXY4DIwZ3oMWs0q+/6sFEewyCxfs6nmH09iR7ZjZwdx3UJ6qYQjQZ8o0M4+Pl6LAE+TPr4Lr4a+a/G7w0SEz+8A5/wAN0xcNqcOGpsSEYDyfO30nZwF1bf/SHOWpvmgceE4hMRSP6+VO03FAS8wgOa3ftcIYgiA++f1mqi/kLAaXOw6rb3KU7OxuBhZNLHd7WqLXWu+HO2XnfjT43hz1yDZDYgSCJ9bh6PZ7Bvs3OcVjspi3fhtGpeXuqyPThqrOd9r8WzXqfylMYpl20ORv9ntr7gqKpK7q4ULRlrd1KTX6579lHDuhA7oS+CJOIdGcjkT+5x2WH0umkckocRo5cZjxA/gjq1wRLsQ+9btF2AIIoMfvhyjVFyGl1PEEX824VRlp5Pyo9awlJxyJSfLKBgf7pr03A0iuW3459sVjClys1DKpbQxnepOhUMnmbGv3MrgkFClbUEaNrKfY0sHaeCtaKGve8sZfebLcTkm8DkY2HYk1dRnVdKRRN1TqO3B0MenkGbQZ3ocuUwDBYTBosJxeGkIDGdzM1H2Prv+Zxce0Dz1A0ikocR78hAQnrEEDuuFwWJ6ex7fyU7/vMdGx761KXQKrRXLKHdY1x2gUe/3YLTasdRY8VRa+PYd9v030e2ORCACe/eytAnZmo9eHvHMuY/f3z55aY4teEgpSdyURxO7FV1Z/19zgVuD9+N3wQ1BeVsf+k7rGXVJNw5meu2/EdXeGwJotGAZDLo23HJZNA42y1AkZUWZWdVVXWNhauQs+M48ZMScNocHJm3CZOvRaM5qmDwMGIJ0gymIIqMePpqRjx9dYv3jJvQl+BObSlJyWHPm0soP1mA2ddC3MX9XM4L7xNH91mjODp/K45amy4slrxgS/Odjv5AKl6RgdQ0pTKqGkulxbzAadc2RdHhU1iCvF3yEbLdiUeAF44aG4pTpjK7mJOrE1tMBIMmtxDaO5bxb98MCCyY/IxLgZhfdCjW8moEUWDQnOmE9WpH9o5jpC7fWz/3JnNSVDwCfYgZ3QOvyEDaDuiAo9ZG5qYjqE4Zp1MmZ8dxl/n6RgU1C+f5RgXpzWQko4GgrlGc2ngI0HITkQM7AZpcR/yks9YjucBZZ+fw1xuxVdbSdeZwfNoEndf1vxZcROQEAelXaOTuNvhu/CZYe99cyk7koioqa++dyxXLntAbfp+O4uQsNj85D6OnGaOnGclsZNgTVzVbHBy1Nlbf+V8KD2Xg3z6ciz+802VMQRAw+VgaeeuCVokJsOmxL8nelozscCIaJKJHdqffHZPOq4uRX7tQUlfupba4sj5kInP4y40MfKBx26+qKl2uHEZNfjmZW45gq5cg0DTVWzawADW5pVr3KYfTJRwU3qc9JcnZWuFVCwVcjmrXXZAqq/hFhTYUDDccpdvVI0n8eLUmtXCgZakF0WRg4IPTCe0eQ2CHCARRpDqvrFlD9cqsIlbd8V9UWWHgg9NI/O8q7DVWULVkrSCKLo1UrKVVHPt+Oygq+wDvtkHI9eEpQRTwaRtEVXaJfk1JcramctrEAPa+aTzV+eUUHjxJ7NjedLt6BOG9Yzm+aCd+MaF0nTm81Xd7Nqyf8yl5+1JRHFph1pXLnsToaT77hb8yYkb3IHX5XrK2HsUzxNfl/9XPhdvgu/GboCq7uJHVIQrUFpS3avDX3jtX98wls5Grv/9XiwqWx3/YUa+fD5WnCkn631oGPTjd5ZxLvrifNXf/F1tFLb1vnkBgB42al9cQ20XzpGyVdRxdsJW+t118XtonBpOxvuEHIEBNYTnOOjuS2cDmJ+eRvno/gihqPXBb8MxFo6QXBx38dJ2LZ9useTnQ787JBHeJojK7mNLUXFJ+3EXe7hR9rHbj+pC2ci9qfViox3WjEI0SYX3iyN9Xz3FX4cDcNYgGEcVOq569Yney543FBHeL5uIPbgfAYbW5iKuJRk3Dv2Entv+/q5Ctdj1ZbfLxZMB9l2LysbD+gU9QZaUZu6emSVxfRet9a7SYtc5bQPHRLFbd8QHj37pFL7gyeJgY9dwsl3GCu0YT3DW6xWc5HxQcSNffveKUqcwqPq8CrV8LokFi3Js3oTjkVnfC5z3mrzKKG26cBR0vHajHdr3D/PGPa0mCSYPtNA/SXt1yZanscLo0+2jJQNoqaoi7uB/Dn76a7tc2MjQi+nXQvHlB28Ln7U7h+Pfb2TDn0/N6rrDesY2a506FzK1HWXzta5zaeJhTGw9p82qqgd8EgiTiGx3CoAen0+eWCSTcNYWIhA6I9WwMQRQI7dMewSiBKNDzhosI6xXLoc83sPjqV9n5nx/oe9tExr93G52mD9aSig9O0xZSQdBojYUVOGqs+s6mAYrDqYXNPLQFqzU46+wUH86k/GQB5acKWXzVq/pigqCFrPQFQBDwDPJpLC4zSoT1akf8pAQi+3dovTq2fixtYiplqXlYQlzzOvn70lh7/9zWr/8VEd4nTvu/IQpaQjnq96Vg/lrGHtwevhu/EQY8MI02Q7pgq6wlemS3M1LMus8aydFvt4CgtRtsjV3R+bLBnFi8i+q8MiSzkbjTYrXFyVmsvO09ZKsDg4eJgQ9Np9NUrcvVyOdncfTbzZSm5JK56bBWCOaQKU7OOq/nSvpknYvHqlgd1BZVcHLtAVeJ49PDL/VGtjwtn7X3zqX/PVMI7hpFVW4J+YmaHr2qQnlaHjEju9Pv9klaP9zMIpI+XYfilLGV17DxsS+ZuexJ2g7SYta5u09QW9LYSObkqv2Up+e79MCVPIxEDe/GoAenk7XlKEmfrm3Gd28KVVEw+3mxfo5rMhUV7DVW+t0xiYOfrscrzJ/R/5lNybFsDn2xAd+oEAY/MgPQPPKL/3sHe95eimiQkCwmcrYlI1sd+MWEUp5eX1wlCMRPTsAS7EvmT4dc5lGwP/2cfpNfijGv/B9Hv92MraKOzlcM/V3CORcKboPvxm8CQRBoO+TMDSsakHD3JcSO64PTaie0Z7tW+fdmPy86XzGUfe+vQLY7WHPPR1y28GG9uUXenlTdG3Va7ZzacEg3+AazkZ6zL8JRp4maKU4ZURKJHtH9vJ7L5GtpJmkgO2U9gdiA7rPHULAvjaLDpzB6eeDh50VVTol2vs3Bzld+bD64qjUjP7XhICXHc7hi0WMaA6XJ+5CtDlKW7CZj7QHCE+JpN6aH625CFJrRK2Wrg5ydx1j7z4+19odKCyGdJgtUm2Fd8Az2pfxkfrPTOl0+hE5TB7moRPq2DSasVyy5e05QlV2Mub5JeXCXKC7+4A6X6xVZYdk/3tI/SyYDZj8vooZ1JWZMT05tOKg/R3C3qObzvAAweJjo+X9n14VUVZVTPx2i4lQh7cb0bFFI748Gt8F34w+JoM5tz+m81OV79XixaJTI35dG3CSNKRPSIxrBoLUgNHiYiOzfodn1RouZqV8/QNqKfZj9Pc+b0THw/mlUZBRSnlGI2deC0cuD3jeNZ8vT3+jniAYJR1UdVTklRA7oyKiXZnNswVYOfrZeU4U8i0asqqj1ORCFgPgIokZ0I7N+QYm/ZAA7XlqIbHOSveMYlacKaT+pL+krExEEAaOXuUWxNUeV1YVH74Imxl4wSIR0jqI6r0wXYNNPk0QOf7mRjpcOdFmEqvPLWHTVK9puQFUZ/sw1xI7t3eKtREnE5OWhy1ALooDRYkIQBMa8/H/kJ6aTumQ3lmBfev5GxU7nikOfb+DA3DXIdidJn6zjsgUP4R0RePYLf0e4Db4bf2qEdIum4mQBst2JYpexVdVqQmGCQHifOMa8NJv0NQcI7dmOzjOGtDiGZ7AvPa4ffcb7ZG8/RllqHm2HdSGgfWP+wTPEr0UBrdrCcvZ/uBoBiBzYibQV+3DW2cnfn8bu1xfjHRFAxIAOlKXmU13v6btAAJ+2QdQWVSIgEN4vTqdxjnrhOmoKyjF6eZD87Ra91y2qyomlu5k2/yG6XjmCqpxiNj3+VbNxz7jASKLWTL0+HyIZRLpcOZRVd32I7bSFQ5UVKrOKcFRbXZLqR+Zt0lg69TuN5AVbWzX4AEMevYLVd39IdW4pQV3aElKvUWMrr2Hfu8spS80lakQ3Nj35FWUn8vBvH06bQZ3oNH3wmfMCFxjpaxJdwnb5ienEuw2+G25cOAx8cDqiQeL4DztAgL3vLMNaWk3f2y8GIGp4N6KGd2t2XQNH3+jtoXdvUlVVkxnwMrtw5I8v3smul39EdsokfrSKS7+8X2+npyoKaSv3UVtcSfsJffGuzzf0/L+xxE8ZgKoonPrpELm7tJ6uikPm1PoknHZHY/KzBQiiyNR5D2oaPUaJuAl9G78TBP0+5acKTrsQFl39iibtrJwmXyCAJdSPuoLTZCNEAdEg4RniS8dpgzjwYaMwmdPq4KtRj7U6T1VWqC2uxORjofxkAWvu/tC1mlYQCIhvXh2aueUI259fgGiQGP7U1QR3aUtdcSUlR7NYOvtNps9/iD1vL6X4yCkUp8LJNQdQVQUUrco5d3cKp346xKSP72p1bhcaYb3ba81WbA5QlF9cBftbwG3w3fhTw2A2Ej2iG6nL92iFRA6ZE0t36wb/dFTllrL3nWUUJKZRV16DKImMff1GQrrFsOLmdyhPz8cS7MuUT/6p5wLSV+7TG3KokkD2tmR2vb6IvD0nkIwGZLsDFW2LP+PHR/V2hw0VxLHjepP0v7U4rQ5NYriF5iWne97+saFUZBTSafqgVp9dccicXJ3ockyrvlVxOlu4h4pm7BvuJQp4BvsSNawr/u3D6XCJtkAd+nwDSnXz5uctQoXdbyxm/Nu38NO/vmgunaCqeAS4tn+szC5h3b2NjJs1//wYpb4gDaAmv5yq3FKs5TV61bF62uKlOGTyE9NIWbyL9hP7uvSZ/a0w4L5LMft5UpaaR+fLh/wpDL6blunGnx6+0SEuVMCAVv7wVFVl+Y1vc3JtIrVFlagOGdnqYOd/fiBl8U7KMwpRnAo1+eXMn/wMK255F0etjbBesUj1jUoQBKrzSsnfqxXmOGptKE4F1amgOBVKjjdXsbQE+nD5D48y9o0bmbHo0eY0O7G5vlBZaj7Lb3ibzM1HWn1uQRKQmsg2aCJj5/DCGgynolJbWEHKop0c/XYzu177kbx9qThtZ26E0mw4RaU6v8yFCdQUSf9bq+kJ1SNtxV6X72W7A7/oYG3+9c/hGexL75vGY6gvvjP7eSKYmtMTd778A6vv+OC85vtrQTIa6HvrRC565R+0qWdJ/dHh9vDd+NPDp00QY1+9gaRP1+PTJpABrQhcOevsmnLmaTFsydzCn4EKhQdPcfjLjfS+eQKIItlbjxI5qBOiQdIXGJdLZBm/di0zNUzeHkT0i2/+hSAQnhBP8eFMnKd5/opDZsPDnzH+rZtb1G8XRJFxb9zE5qe+RpVVBj9yORsf/xK57vwNdlV2CdX55Zxce0CXLD591yEamjcTB61Q6fCXP509P1AP7/AAkASo1wLybx/OxPduY9fri3HUWOl7+8UYPc2EdIvmyqVPUJ1Xin9sGNV5ZRQmnSRnd4q2s1E19lXhoVM4am1/KfrkhYLb4Lvxl0CbwZ1pM/jMtE+jp5mQ7tGUpORoVbaKiiCJBHePpuPUgaSt3KcxV+qNlirL2GutCJJIwYF0yjMKKD9ZQOSAjlgCvaktrtTPlcwGJrx/O16h/meda+y4Ppz6SaMbekcEMPGdWylLz2fnKz9SkJjmGrqwO1n3wCdct/nFFumpEQnxzFz+lP7ZPyasOftGAFFq2Vg3heqUkZvq3qgQ0iMG2eYgqHNbQrpFU3Aog7Rlrh66s85OxoaDGMxG19oDAFGg7+0XY/b11A/FTU6g8HAGGeuSCIiPZOybN2Ly9GD0i9c3m5OHv5cuZe0fG4Z/bBgdLh1A/t5U6ko12WaPAK9Wk7e2qjq2PP0NZam5dL586FmT8391CE3LpH9vtO/aU33+6xW/9zTc+AvDabWTumIvRYczSV+9v74oy0jCPZfQdeZwKk4Vsvymd3DWOTBYjFz6xf1IZgPzJz3TKHsgCMza9AKlKblaeEKAXjeM0xOpZ4OqKJzaeBh7VS32ahvW0io6XDoAv5hQipOzOPC/tS5FR4IkcsWSxzF5W87aISxx7hoSP1h59kkI9e540w6Pkkhwlyhd0qDhmCorGDxMTJ33AJLJwPeXvajLUjTANyaE6BHdSV64VafJGiwmRr14PdEtJM1bg7WsmqrcUgLah5+RgVOZVcSet5cB0P+eKfhGhbR43qYnvubk2kQUh0bNHffWzUQktLDT+pPjmr5R+1RVPSun2O3hu/G3gsHDROfLhlCdU6obJqfVobX2A/xiQrly2ZNU55biHRmIwWxEtjuRTEbN4AuaR2n0NBPepz3hfdqf8X5Oqx3JbHTxzgVRpN2Ynmx9bgFpK/ci2xwkL9zGjEWPEtwlirGv3sC2FxaSumwPAN6RAXw3/QUEQWD0i9cTPVIrDqvMKmbXaz8i2530v/dSgjq2oce1ozRaZFVdq6qafu1C6T5rFIpDZscrP2jnCdBj9mjaDunC6rs+RHE4URW1saBM1JQ3PQK8EZv0CQAweJoZ9sRMwvtojUF+evgzyk8W4NcuVOtuteMYA++b5pK7KEvPp/RYDmF9YnXuetGRTFbe9j6CoDV9mTbvQZfmKU3hGxXCRa/844zvXntHRU0WavQG5H9XuJO2bvwt0W5sL63JiYcRycNI/OQE6kqrKDyUgaoo+MeG6cwPyWRg4vu3EdI9hrDe7Rk0ZzorbnqHlbe9T/nJghbHt9dYWX7TO3w5/BG+nfg0lU304xuQs12TFmjwskubJHwHPXQZseN7IXkYqTxVhGJ3ItscbH/pO/2clbe9T9bWZHJ3pbDy5veQ7U4MFhMzfniUIY/MoOvVIzQdHklAbKICKogiHaYM0JRCG2SlVSg6nEl4nzgu/uAO+t52Me0n9sNQn6yWrQ5yd5/Av31YfTN0CclsoO3QLly59AnC+8QBYAnwZtJHdzHwgemUHM2mPC2flEW7OPj5ev3+eXtOsOS619n24kJ+uPJl/R0m/W8tzlobjhobtvIa0lfvP9+flZqCcva8vZQDc9fgqLXRc/ZFet8Co6eZqGFdAag4VUju7hSdffV3gdvDd+NvieAuUVz61f3kJ6YR0j0Gxe5k4aXPaZWenmamfjPHRc0zpHsMl3x+L7LdybxxT2gyxAKsuv0DJn5wOztf/RHVKTPggWmossLyG9/R5X3rSqpY/9BnxE3oS/yU/jpdM7xfPBnrk5BtDlRVJSC+UeCisAaDAAAYpUlEQVTs2MJtpC7b56olD3pPAEVWqMlvpEA66mzYKmrwDPHDw9+LzpdrRWb9br+YnN0pbJjzmX5u+cl8cnYeI7iLq1RB8ZFMrOU1hPZsR2jPdqiKQuLcEA7MXY0qq6SvSURxykybN4ddbywic/MR8vensfja15g+/yE93GSrqiN5/hbdmMo2R6NWDnDsh+367koQBTI2HKT3jeOwBHrriWFBEjH7t+zdtwbZ7mTJda9jLa9BEAVyd6Uw6eO7mPrVA1RmFRHWuz1mX0/SVu1j67PztR7EQb5MnfeAXovxV4fb4Lvxt0VDEhBg3f1z9YSjxm/fT9erRjS7xlZR0xjOUKG2uJIVt7yLtawaVK1na0BchIv+O6pK2Ylc9qbmc+iLn5i5/EkMFhPDnphZzz4ppfMVQ106OpWk5DQz9iZfT0Y+d602R7vThRWjygqmJonRBhi9PDD7eJ6mh69p3Yf3jcOnbRAVJwvrx1DJ3HyYjpcOBLSdQFDHSIweJq3Gwe6k6Egm3hEBlJ3IQ3XIOB0ygiiQvz9V1yFad+/HFB3NbLyX2UCnyxurnAPiIsg0H0G21TcEr1ejTLh7CuWniihNyaHdRb2IHedanXvgk7Wk/LAD/7gIRj57rUsiGLRwjaPWpkkwy1B4MANw/Z0BDny8RutyBqhqJXl7Tpy3htKfFW6D74YbgCXIF9EooTjO7F1agn0J6Rat8e1VlbZDu5Cx/mBjw2yrveVAqQqoCraKGvZ/uIoB916KZDLQ64aWRbo6TRtE6pLd+meTr4Vr1j2LKImoqkr6ugMu5wsGsZnWDWiUycS5q/EI9NF7DEQN66rTPIM7R1GVVaIxeATwDHZtJh/aKxZBEhGNBkSDSHx9Ry/fqGAqs4u11pFO2UVDpjg5W68ilkwGRr8024WS2nP2RdSVVVOwP412YxsNu9nPi8mtVM7m7k7h4CfrcNbZqS2qZMfLPzTTw/cKD8DoadYE5iSJkO4ta+N7hWk9jlVZAUVxWWj/6nAbfDfcQPMuKzOLKEnJod1FvWk/vmXtF0EQmPjB7WRtPoJolGg7tCvrH/yEvD0nAAjuGsWQf13Bqts/oLaogqiR3ajKLqE8rTGkkb56PwPuvfSM8wnrFcvED25n/wcrMflaGPTgZXq8PfHD1RrvvaGfjFFi2FNXNyvospZVs/quD3HW2REkkaAubbnks38iGhr/7AfNmY61ooay1Dw6Th1Em8GdyNtzgj3vLMPsa2HoY1cy7Zs5nNpwEO/IQD1hHNwjhpwdx1DrKZ9N+xJHDuxI7q4UFFnG7OeptxtsgGiUGDznsjM+/+moyS/Xn1dxylTnNtcfMpiNXPLFfRz9dgtGT7NL/4OmGPHMNfz06JdU55TQ/bpRzUJbf2W4aZluuPELoThlMjcfQZUVokd117X+G3rtFh3NYtn/vYkqK1pTk16xBHeJoqaogp7XjyaoSxQZ65KoLaogdlzvs3qcP858Wa9qNXiaGfrYlcRN7NvsvJJj2Sy/+V29oMvoZea6zS+dcWxreQ0LJv9b26kIAv6xYVy28OFm531/+YtUZGihIKOnmeHPXEO7MT0BLZZ+fNFOHNV1dJw6CEuQz1neoPaujn67mZLkbOKn9G9WuWotr+HHmS/jrLOhyAqjX5xN9Ihzp3v+1eGmZbrhxm8E0SDpxs7leL1HHtI1ihHPXkvS3DV4hQcg250kL9yK4pDJ3pZM/MX9SF2xF1VWSPpkLZf/+NgZ2yyG94unMqtYS/YqCsGtSEn7tw/HEuhDXT3tMm6iFo5xWu1krE9CNBpoN6anS6/YuuLKxu5Tqkp1bss0xsCObajKKUFxyKiKgl9MIw9eMhnoeuWwM76z05E0dw2HvtiA0+og46eDTJ57t4vn7eHvxeXfPULhoQx8o4Jb5d27cWa4Db4bf2vk7Uslc+NhQrpHEzu+T6vNVn4p4ib01RUvvxz5L50bLggC6esbu2OJRgMlyVktSik0YOB9U/EM9qEsLZ/OM4a0KucgmQxM/ep+MjYcxOzrSfSo7qiKwopb3qU8XaNCpq/az9jXb9Sv8WsXqsXns4oB6DB1YItjD3v8SowWExWniug+axQBcRrDyF5tpfhoFr5RwXhHnFshGkDunhM465k7qBpj6PRQi8nHQtshXc55TDeaw23w3fjbovDQKdbc85HeAtFebdXpjOcCW1UdxxZuBaDzFcPOqfl59vZkF/kBQRQI6RpN3p4TmrcsK/hGn9l7FY0SEf07cuz7HWRvP8aA+6bS8dIBLZ5r8rHQsYnRri2upOxEns40ytys9d6NSOiAydsD0SAx5dN/krX1KCZvC5EDW154jF4eDHvyKpdjdWXVLLrqZZx1DlRZZuwbNxM5QGs6U1NYjq2iloC48GZCcQAxY3pSkpyN02bXehm0pDvkxi+G2+C78bdFQWKaLr/rtNrJ2nLknA2+qqqsuPFtKjK1gqr0VfuZNv+hs+4Q0lcnurRDjJvUj353TGbfe8upziujx+zR5yTRsO6B/2EtqQJgx4sLaTuks0vitDWY/byQ6quHG7iam5/8GqOXB9MXPIzZx4LBw3TGhiWt4dRPB7FXWXVKatKn64gc0EHjvf97PoIoENwtmonv3eYSRgLodvUIvEL8KEvLI2ZUDxcapRu/HtwG342/LUJ7xSIaRGSnjMHDSJtz7LkL4Ky1UZ5RqBvv8oxCHDW2s2rdhPSIIWNdEk6rHYOHSfesBz98+Tnfu7a4Ujf2oJFXWtTYbwGSycCkj+9iz1tLKTx4EkeNVtmqqpC783gz7vvpKEvLY/9/V2GwmOh/9xSXBLNnsC9CfXN20SDhHa4Jye15a5m+CBQfzaLw8CnM3hYQBb17mCAIxI7rfdb7u/HL4Db4bvxtEdYrlrGv30jG+oOE9oghfkr/c77W4GnGOzyA6vpqV+/wAIxeZ6/W7Hz5EJxWO7k7U4gZ06PFZO/ZkLJoJ4iCrpXjGeyrFy+dCwI7RDLh3VtZ/+AnZG05ou1yFAWvs+wsnFY7y296B3tVHYIoUpKcxWULH9G/jxreja5XDefEsj0EdojUZarNvhZqC8sBrUDs6DdbyNqq6fx3vnwIA1uRsz4fyA4nPz3yOdnbjxHUMZLxb9+C2c+L6rxStjzzLXWlVSTcOVmnlf5d4Tb4bvyt0WZgJ9o04YnLDifbnltA7q4UIgd2ZOjjV+o0y6YQBIEpn/6TpE/XAdDz/y5qMZxjq6ghdflejF4exE9KQDRK9Jg1mh6zfr5Mr9HLA8kgIdudGs2zR8zPSjYPfXwmm5+aR0VGId2uHkFofS/Z1lBXUqWFglTNcDfQMhsgCAIJd00h4a4plKXmseS617GVVdNx+iCcNge2smq6zxpN4tzVemHW0W82k3DXFCTTzzdFqqqy9+1lZG9LRnHIFB/LYf9/VzH44ctZ98AnlKbkgqry07++YMaiR89Jwvqvil9k8AVBuAJ4GugCDFBVdW+T7/4F3AjIwD2qqq5ucRA33PgDIXn+Vk6uPYBsc3By7QECO0TQvRXjbAnyYdCD01sdS3Y4WTzrdWqLKxFFgawtR7jo1Rt+8Rw7XTaYjPUHKEg8iaqqZGw8xMn1ScRe1KvVa9LXJnL4y434xfx/e2ceHVWd5fHPrcpKEkkCBAIoa6CFQZahEdpuRgGBQZYR2xm0j4I62k4PRznap9FhjkfG8Tja0/Y4nhlt2oZGj2KLijC0rK2tzSqLAcGwhLCFRAgkIRtJKlW/+eO9FJWiihSkliz3c06devV+v/feN/e93Pfeb7k3i3G/mE1CWjJJ6SlMfu1RwEr9uG/ZZlK6pzNg6qiAHaspPTJIzc6kqqgUESH7+zlBj/f5v7xNpT3SJ++Drcx692nS+3XHXd/AvmWbcTfOxE2MxxHXshiOe9/4lLwPtnjj/Ru325thq7q4zBtTQpwOakoq1OG3gAPAbOA3vitFZAgwBxgK9AQ2i8ggY0yIiTIVJTZUny33tje761xUfVd+3fuqLLxAbVkVnvoGPMDpLXlh0RiXGE/moF6c238S4/bgqWsgf+2uoA6/9GgRf3l+Be5aF6VHzuCudzHh5Xne8tqyKlb/5D9xVdfhjI/jQl4htz59ZTOLw+lgxu8XcGzdHuIS4xlgh1nw5/SWb6ksvDwTVhxihWvG6kOY8MuH2PrC+yDC+MU/CXhzuRYOfbS9SXKXuOREhj9yJwBD7hvPN8s/A4eQ1jOTzEGtP+9sJGmRwzfG5AGBXidnAe8bY+qA4yKSD4wBtrfkeIoSaQbPHseR1Tu8I1iuZZimPynd063JV2I5y4yBPcKicffrazn88Q5vh7EzKZ5uQy/HjfG43Bxdu4v6yksMnD6aitPncTgcuO0y/9yz5/NOe2PfN7itSVmBHD5YqRpvvvc2729jDAff+4KCDV/TfUR/bvzhzXz2i2W466xhn+J00G3oTXT10XfjbTczZ/3isNgCoPNN3SipvIRxe3AkxDHznadIt+cmjHxsCr3GDqa2vIqeYwYFbJ7rSETqr+8F7PD5XWivU5RWTXq/7vz4k0WUHi0iM6cnyZnNhwUIRnynRO5a+gS5b20kITWZUT+bFhaNB1d8icdlR+wUIWfmrdwyb6K3/M//+g6FW77F4/ZwcMUXzFi+AGdiPMZYGa5yZozh2w+2kJCaRP8po0jv3+PyzSMhjqzhfUPSceqLAxzflMuJz/bjrnNRll9MWX6R19k3cudrj16Oux8BJrwyj20vfUjN+QpGPT7V6+wbybqlb8SO3dZo1uGLyGYg0KPJImPM6mCbBVgXMGiPiDwGPAbQtYfeE5TYk5yZ1qQjtyVkDMjmjpfmhmVfjSRnplJVbI0OcibEMeqnU5uMay/cmuedtVpfVUvdxRruXrmQM9vySO6WztYX3ufShUpEhMKtedz+4gNMfeOfOPjuF6T17sKIRyY3qyFv5VZ2/dcaGupc3jZyd53rcnYpL4a6ihrikoKnK2wpnbp1bjJbWAlOsw7fGBM4fuvVKQR850X3BoqC7H8JsASs4GnXcSxF6VDc+dqj/OX5FdRX1XLrU7O8Sb4b6TK4FyUHTuFxW7HqU7MzSUhNYuBd36csv5ja8ipvP8VJO3du1rC+ZP1H35A1FGzY2yRblCPeicPpYNi8iXjcbkoOnEIcVvC1UCaEKdEhUk06a4D3RORVrE7bHOCrq2+iKEooZAzIZuY7TwUtn/Trf2Tvb9ZTV17N8IcmNZkMltI93dvnJnEOMgZc+fLuqq7l82ffpuTgKfrcMYwfPHvvFU0yPf56AOfzTuOudeFIiGPYA3fQd8ItdPleb3qNGUTBxr246930nzqyxZ2ySvho6bDMu4HXgW7AH0Uk1xgzxRhzUEQ+AL4FGoB/1hE6inLtXLpQebk/IYQwwwCJN3QKGm8+IS2ZaUvm8/VvN5B4QydGPzHjijp731xP0VdH8LjcFKzbQ/cR/cnxm5Q28tEpxCUlcGz9Xi6dr+T8wVMMvc/KEOaIdzLwrtAnsSnRo6WjdFYBq4KUvQi82JL9K0pH5cz2QxzflMux9XvshCWG6cue9EalbAldvtebSb8K3uZdU3LR2xbvafBQW1p5RR1HnJPuI/qx761NNNTWU7z7KNte+pAJr8xrsT4lcui7lqKEkeObc1k5899Z88CrV8xEDZXCbYfY/POlHFm9E3ddA67qWlzVdRz+ODqjmoc9eAdxnRKJT0kiIS056Hj76rMXvR7E0+ChMkAWKqV10bEHpSpKGKkpuciXz72Hu85FZdEFNj/9O+756Nlr3k/htjzcta4m65yJ8aT45I0NhMftoa6ihqTOnVrUbt51yE3c+8kiLp4qITOnZ9CAcL1vu9lOkC543B6GP3zndR9TiQ7q8BUlTFwqq/JGi8TgTRp+rWSPHsjhVdtx17oQp4P4lCRu+puhDPmH4Fmkqs+Vs3bea1wqrSS1ZyYzlj1JYueUoPWbI7lLWrN9BolpycxeuZBz+0+Q2qsLnZuJ46/EHnX4ihImMgZkk5nTk9L8YozHw189OOG69tPn9mGMX3w/hVsP0XPsIG+mrKuxf9mfqDlfgXF7qCoqJe/DrSGNp28p8SlJ9BoXelhpJbaow1eUMOFwOpi2ZD5ncwtIuKETXQZf/0TCfpNGhJyExFVdS9mxYmsmLQCCw+m86jZKx0QdvqKEESv9YPAokuHGGMMfH3md8pNnvTNeMwZmN4l3oyiNqMNXlAhTVvAdhVvyyMzJDnvzR115NeUnzjYJaTB96RMtii+vtF/0qlCUCFJ+/Cz/9+Cv8bgacMTFMXbhPUETjl8PCTd0IrFzCpdKrdg4KT3SccRfbs65ePIcFw6fIWtYX1Kzm8+Vq7Rv1OErSgQp2nnYilnf4MHTUE/Buj1hdfgOp4PpS5/g6yUbEIeDUY9P9YZO+O7rAjbOfxNxODDAjOULvDlklY6JOnxFiSCZg3t7h2o6k+LJGt4v7MdI69WF8Yvvv2L94VXbvVEzETi+KZeMn04N+/GVtoM6fEWJID1G9udHi+8nf+0uug7tw/CHJja/UZhI75uFMzEed52LuMSEa0p0rrRP1OErSoS5liGW4WTYAxOoKamgeHc+fSYMCxoiQek4qMNXlHaKI97JuIX3xFqG0orQ4GmKoigdBLk8Oy/2iEgJcLIFu+gKnA+TnEijWsNPW9EJqjVStBWt4dbZxxjTbDCjVuXwW4qI7DbGjI61jlBQreGnregE1Rop2orWWOnUJh1FUZQOgjp8RVGUDkJ7c/hLYi3gGlCt4aet6ATVGinaitaY6GxXbfiKoihKcNrbE76iKIoShDbt8EXkDyKSa39OiEhukHonROQbu97uaOu0NTwvImd89E4LUm+qiBwWkXwReSbaOm0NvxSRQyKyX0RWiUh6kHoxsWtzNhKRRPvayBeRnSLSN1ra/HTcKCKfi0ieiBwUkScD1LldRC76XBfPxUKrreWq51Ms/tu2634RaT4VV/g1DvaxVa6IVIjIAr86MbOpiCwVkXMicsBnXaaIbBKRo/Z3wLClIjLXrnNUROZGRKAxpl18gF8BzwUpOwF0jbG+54GfN1PHCRwD+gMJwD5gSAy0Tgbi7OWXgZdbi11DsRHwM+BNe3kO8IcYnfNsYJS9nAYcCaD1dmBtLPRd6/kEpgHrAAHGAjtjrNcJfIc1Br1V2BQYD4wCDvisewV4xl5+JtD/E5AJFNjfGfZyRrj1tekn/EbEigf798CKWGtpIWOAfGNMgTGmHngfmBVtEcaYjcaYBvvnDqB3tDVchVBsNAtYbi9/CEyUxpjBUcQYU2yM2WsvVwJ5wPXnPYw9s4C3jcUOIF1EsmOoZyJwzBjTksmaYcUY8yVQ6rfa93pcDvxdgE2nAJuMMaXGmDJgExD20KbtwuEDPwLOGmOOBik3wEYR2SMij0VRlz/z7VfhpUFe63oBp31+FxJ7B/Ew1lNdIGJh11Bs5K1j37guAl2ioi4IdrPSSGBngOJxIrJPRNaJyNCoCmtKc+eztV2fcwj+kNdabArQ3RhTDNZDAJAVoE5UbNvqg6eJyGYgUNaGRcaY1fbyfVz96f42Y0yRiGQBm0TkkH0njppW4A3gBax/qhewmqAe9t9FgG0jMowqFLuKyCKgAXg3yG6iYlc/QrFR1OwYCiKSCnwELDDGVPgV78Vqkqiy+3U+AaKXFLcpzZ3PVmNXEUkAZgLPBihuTTYNlajYttU7fGPMpKuVi0gcMBsIGvvVGFNkf58TkVVYzQJhd0zNaW1ERH4LrA1QVAjc6PO7N1AUBmlXEIJd5wLTgYnGbmQMsI+o2NWPUGzUWKfQvj46c+VrdlQQkXgsZ/+uMeZj/3LfG4Ax5lMR+V8R6WqMiXo8mBDOZ9SuzxD4W2CvMeasf0FrsqnNWRHJNsYU201g5wLUKcTqe2ikN/DncAtpD006k4BDxpjCQIUikiIiaY3LWB2SBwLVjSR+bZ13B9GwC8gRkX72E8wcYE009PkiIlOBhcBMY0xNkDqxsmsoNloDNI5y+DHwWbCbViSx+w1+B+QZY14NUqdHY/+CiIzB+p+8ED2VXh2hnM81wIP2aJ2xwMXGpooYEPStvrXY1Aff63EusDpAnQ3AZBHJsJt7J9vrwksserLD+QF+Dzzut64n8Km93B9rJMc+4CBWk0UsdL4DfAPsty+AbH+t9u9pWKM5jsVQaz5We2Ku/XnTX2ss7RrIRsC/Yd2gAJKAlfbf8RXQP0Z2/CHWa/l+H1tOAx5vvGaB+bb99mF1kP8gRloDnk8/rQL8j233b4DRMdLaCcuBd/ZZ1ypsinUTKgZcWE/tj2D1H/0JOGp/Z9p1RwNv+Wz7sH3N5gMPRUKfzrRVFEXpILSHJh1FURQlBNThK4qidBDU4SuKonQQ1OEriqJ0ENThK4qidBDU4SuKonQQ1OEriqJ0ENThK4qidBD+H6jbbaVRia/nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22ebc2c0748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Z = Z.reshape(xx.shape)\n",
    "plt.pcolormesh(xx, yy, Z, cmap=plt.cm.Paired)\n",
    "plt.scatter(X[:,0],X[:,1],c=y,s=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Online Learning Models\n",
    "* Stochastic Gradient Descent & Passive Aggrasive Algorithms\n",
    "* Simple & Efficient to fit linear models\n",
    "* Useful where number of samples is very large ( Scale of 10^5 ) \n",
    "* Supports partial_fit for out-of-core learning\n",
    "* Both the algorithms support regression & classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_classification, make_regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "X,y = make_classification(n_classes=2,n_features=10,n_samples=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "trainX,testX, trainY,testY = train_test_split(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import SGDClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "sgd = SGDClassifier(n_iter=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7904"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd.partial_fit(trainX[:1500],trainY[:1500], classes=[0,1])\n",
    "sgd.score(testX,testY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8116"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd.partial_fit(trainX[1500:5000],trainY[1500:5000])\n",
    "sgd.score(testX,testY)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6. Robust Regression\n",
    "* Robust regression is interested in fitting a regression model in the presence of corrupt data: either outliers, or error in the model.\n",
    "* Three techniques supported by scikit - RANSAC, Theil Sen and HuberRegressor\n",
    "\n",
    "#### Comparisions RANSAC, Theil Sen, HuberRegressor\n",
    "* HuberRegressor should be faster than RANSAC \n",
    "* Theil Sen and RANSAC are unlikely to be as robust as HuberRegressor for the default parameters.\n",
    "* RANSAC will deal better with large outliers in the y direction\n",
    "* RANSAC is faster than Theil Sen and scales much better with the number of samples\n",
    "* RANSAC is a good default option"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_samples = 1000\n",
    "n_outliers = 50\n",
    "X, y, coef = make_regression(n_samples=n_samples, n_features=1,\n",
    "                                      n_informative=1, noise=10,\n",
    "                                      coef=True, random_state=0)\n",
    "# Add outlier data\n",
    "np.random.seed(0)\n",
    "X[:n_outliers] = 3 + 0.5 * np.random.normal(size=(n_outliers, 1))\n",
    "y[:n_outliers] = -3 + 10 * np.random.normal(size=n_outliers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression,RANSACRegressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RANSACRegressor(base_estimator=None, is_data_valid=None, is_model_valid=None,\n",
       "        loss='absolute_loss', max_skips=inf, max_trials=100,\n",
       "        min_samples=None, random_state=None, residual_metric=None,\n",
       "        residual_threshold=None, stop_n_inliers=inf, stop_probability=0.99,\n",
       "        stop_score=inf)"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr = LinearRegression()\n",
    "lr.fit(X, y)\n",
    "ransac = RANSACRegressor()\n",
    "ransac.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x22ec0056400>"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22ebfd115f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X,y,s=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "ransac_pred = ransac.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr_pred = lr.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x22ebff4ea58>"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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8+fLWfDxA8LLcCkVr0HVJSbWNeFmKeOtPsDevcaP+Pa9UdHvSa3wEcaFxZCZmYhAGMhMziQuN69DnT5gwge+//55t27YBYLVa2bp1q2/Qj4+Pp7q6ukmns8FgID8/n/z8fO69995G54cNG0ZRUZFPCOrq6ti4cSMxMTFERkayapW7pO7SpUub7OPUqVNZtGiRz3exZ88eDh48yN69e7FYLFx88cXcdNNNrF27lurqaioqKjjttNN44oknyM/PD7hXVFQUMTExPvv/a6+95lsdKBS/F93l4up//ZeCR4+Bx0ci/UVAaHD+q3D9LzB7eY+tFNoe9JoVgRCCRVMXUWorJS40rsM3eUlISGDx4sXMmDEDu90OwN///nfS0tKYNWsWo0ePZtCgQYwbN+533T8kJIR33nmHuXPnUlFRgdPp5LrrriM9PZ2XXnqJWbNmER4eznHHHeczWzXk5JNPZvPmzT6TVUREBK+//jrbtm3j5ptvRtM0TCYTzz33HFVVVZx99tm+TXMef/zxRvd75ZVXmDNnDlarlcGDB/Pyyy//rvemUHhXAVFL/49/Fa1CCN+W8fWkTIT0s9Qq4HegylD3Aqqrq305Dw8++CD79u0LGoXU1VDfsQLcInDRwh+oKPiZ/4bcitETDuoducSAsXDhmyoxLAitLUPda1YEvZmPP/6YBx54AKfTSWpqqtrQRtGtKKm2cf3eG8g2bcUqQ4kUte4TA3MQ099QAtAGKCHoBUyfPr3Z6COFoquhu1yUFu0lLqE/8dYdxGi/YkRH4IArVyC8FUJ7qADoUqe4thgNjbiw9jdld2shkGpD9x5LdzBZKtoH3VnHrw8dw5GOrVi1UCzShsEcgayzYkgej+g3qscKALhF4PL/Xc7ag2sBGNt3bLuGu0M3FoLQ0FBKSkqIi+t4x6+ifZFSUlJSQmhoaGd3RdHRuJw4Fx5PmuMXhACDbnWP+Y4amLMCEkf0aBGA+lB3L+0d7g5tIARCiGTgVaAfoAMLpZRPCiFigbeAQcBO4AIpZZlwj9pPAqcBVuAyKeXaQ31uUlIShYWFFBUVHe5bUHRBQkNDSUpK6uxuKNoYXZeU1DiIjwgJnMDpOlTthyUzMB1cjxDuUkG1WhhhOBApE3qkCOhSbxTJ6A11964IOiLc/bCjhoQQ/YH+Usq1QohIIA/4P+AyoFRK+aAQ4lYgRko5TwhxGnAtbiEYDzwppRzf3DOCRQ0pFIruha5LZrywirxdZWSnRPP0jGwS+5gRugsWnQJ71vjaSqAuMQPT7OUIW1mP2TbSO/DHmGMosZVwy7e3BK120FY+gg6LGpJS7gP2eX6uEkJsBgYCZwPHeZq9AnwNzPMcf9VTB2OVECJaCNHfcx+FQtFDaDj7L6lxkLerDKcuWbOzhDMfeo/BySksMd4Ne9YE5AWI/lmEzPIkhfWQbSO9ZW7WHViHxWTBWmdFRwcam380oZFo6bj33aY+AiHEICAL+BHo6x3cpZT7hBDedzUQ2O13WaHnmBIChaKH4D/7H5saw5JZE4iPCGFsagzrdu7lfePdpGmF/LzvSNC2I3CbgqQAMSAHccUXPS4z2Gv719Gprqv2He+sagf+tNknLYSIAN4FrpNSVjbXNMixRvYpIcRsIUSuECJX+QEUiu6F/+w/b1cZJTUOhJS8cf4ANpv/zEitAJPQydB2UNcvC6cUrNWHMNHxLMUXftztRcCpO9lcspktJVvQdfes32v719CIMEVgEAayE7NZdv4yXp76cqcGvbTJikAIYcItAm9IKd/zHD7gNfl4/AgHPccLgWS/y5OAvQ3vKaVcCCwEt4+gLfqpUCg6Bu/s37siiLdoyJdOxrBnDUh8zmCZMAzTrM+58vnPWV4oGZsaS3ykueUHdGGcupNjlhxDjbMGgHBjOCtmrMCoGX1lbmLMMZTZyzql3E0w2iJqSAAvAZullI/5nfoQuBR40PP/D/yOXyOEWIrbWVyh/AMKRc9CCMGSWRMoqbISX70V+dyxiOJNbnOARwRcArRZ3yAMRhbMOTV4NFEXR5c6JbUlAMSHxSOEYEfFDp8IANQ4a9hRsYO0mDQ0ofn8AO0ZDnqotMWK4GjgT8DPQghv8OvtuAXgbSHETKAA8Baj/wR3xNA23OGjl7dBHxQKRTvTZOhnE+c1l52EZ4Yi62oQUO8HADbryZzlvJ9VDkmCGTRNkNDNVgJe52/eAXcF1OzEbF4+5WWGRA0h3BgesCIYEjWkM7vaIm0RNbSC4HZ/gBOCtJfAXw73uQqFouMI5vzVtPo/e6dT54KFK8kvKCcruQ9vX3QEhn+Ngzqrb3CQEjbpyVyt3U6hsw85g+KIjwjpnDf0O/GP+28u8WvFjBX8WvYrGhpDY4aidXGfR7fNLFYoFB1HMOevdwav65JpC1eSX1BKAmXcvv8u5JPbkNTPECVQg4k7E//Fl1cdTVmts9uYgbyDf1RIFJf97zI2FG8gq28WL538EpmJmb4VgX/kj1EzMiKu+1TOVUKgUChapJHz128mX1LjYENhCe+Y7iJL+63eDIR7FQCwXRtM5F9X8G60BSEECZGGzngbh4QudQ5aD3Lj1zeyoXgDYcYwn7ln3YF1lNnLWDR1USMfQXdECYFCoWgRn/O3gY9A1yVSd/FR2N9Jc/7mS/6VwFrXYG6vu4ISoigmmh8Nhm4xUHodwDd+fSPritb5jvs7gEfFj/JF/CRYEjqjm22KEgKFQtEs/k5grznI6dTZerCKez74mcrdG/goZEuACMiEkfxdPsyWwvqUoq4vAfUOYO/+5v5YjBZsThujEkbx2imvdQtRay1KCBQKRZM4nTrTFq5kfWEFOR4nse5yMfX+JcTb9nK96T3GmrZSI8OIxL1hTDWh2P74JW+Hm8m87wtqHC4izUbiwrueY7hhTR+vA7ihCGTEZ/DKKa9Q7ijvMrH/bYkSAoVC4cN/9i8lXLBwJesKygHI3VXG1v0VJP/nPJbJXPBEe7r3D3Zwc8zTbDxQQ5/kDJZGhVFc7cBW5x5QrQ4npda6LhMi6tSd/Fr2K/f8cA8bSzcC7rr/XgewtxDcQ5MfwiAMvsJvXSn2vy1RQqBQKIDGIaJPTM/0iYBAJ9lUzuNPP8az5tx6M5AEKQwYUibw8CUXU2Kt8/kQ4iNCyBkUG9TB3Jk0zPz1kn8w3+cAblgauqejhECh6MX4rwD8Q0Rzd5Zy1et5SMCAgw/M80lnF4TUF4cDQGiI6zZCn36eaKD6GX9TDubOwOa08V3hd/wh6Q/sqNrRSAQA0uPSfYN/T535N4USAoWil9JwBfDmFeN9IaKjB/bhp90lpLODt81/x4IzcDuAc19CRPSF1ElgaDoUtLMzhnWps696H6e8d4rv2I8zfgzI/AUYFTeK107tWQ7gQ0EJgULRS2mYJFZqrfPN4J2OWiKeSiMCO0CAKQghEOnnNCsAnYW/8zcmNIaZn89k7YHADRC/3/s9K2asYFv5NmJCYtA0rVvnALQFSggUil5KrMXE6KQo1hdW+Gz4Qkri9FJ2/OsM+mEPFABgkz6Qu/su4C2htV0N+zbC5rQx4+MZbCvfBrgjfTaWbEQ2qHL/h6Q/YNSMDI8d3hnd7JIoIVAoeiG6LrnoxR9Zv7ucMcnRvH5ZNqXb1xK7/GbE3nUMlrqvVDSAC8EE+5MUE4dhT1VAiYnOxLsCcLqcnPreqb4dvwA2FG9gVMIoNhZvZHTcaP6U/ieOTzoeo1ENew1Rn4hC0YNpqmKo1yzkkrBp917qHkgmVtpBeMpDCHBKwS+kcK/9IlYzEnCbgsamxhBrMVFUZe8UJ7A389elu7j+q+vZULohaDtvPaCuVPe/q6KEQKHooQSrGApuEYgLN5GTEsWegk18HXITmiQgM1gMyKH8zJcZHj+Auhd+xFBYQcbAKBZcnE18hJmLXvyxyUqk7fJeGhR+W1+8vsm2Ghqfn/s5iRGJvTIC6PeghECh6KE0dAYXVduZu2QdebvKGJccyZvyDkSIu4yyvy/AGT8C0xVfEO8pnfzunEkBq4qiKnuTlUjbA/+yD6GG0KChnwBZCVn8Jesv5CTmYOiCjuyujBIChaKH0NAMFB8RQnZKDHkFZWSnxiClJG9nMTGygpv33YHwbBoP9b4AqzATNue7gD2DG4aANleJtM3ei2cFEGOOYXvFdl/Zh2AiMCpuFE/94SniLb078udwUEKgUHRzdF1SVG3n2iXrWNvADAQSXZfUWGu5ffH/eMv4dzK0bRgFASKgA6fa72O7NpicRbnNmnvaM1FMlzpF1iJu+PoGNpZsdJd+rqsh3BROrbPW93pU/Cgen/K4Cv1sI5QQKBTdGK8fIHdnKS7PrN5rrnHqOqt3lmHCymOlNzBU24/QPBvH47cKwES6/UXABDqtMve0ZaKYN/JH13Vu+PoGfi752Xeuuq7a3cc6K/8+698cGXWkcv62A0oIFIpuTEmNI0AEBJCdEk10qJHs+5cRSjmbzFe7N4vxcwbX9c3mmF2XEY2VrSQBGlnJ0fy8p6JD6wLpUufy/13O2oNrg54PN7pXAll9sxgaPVQ5f9sJJQQKRTfCuw9AXHgIiX1CibWYsIQYqbI7AXypU78erCTStovvzTcDgSJAYjqm2csYuGAl63ZX+O59w0lDSOvbh8Q+oe0623a4HKw9sJbBfQYjNBGw768/o+NH8+opr/bY0s9dCSGlbLlVJ5OTkyNzc3M7uxsKRafidOpk3vc51XZ3aeejBsXw5IwsJj2w3CcAGk5GiF283XcJlrJNAAGJYVYRStjf9oDBQFGVjdmv5vLTnvrNYyLMBvLvPBmjsW3zhr3mH4fTwanvn+o7np2YjZQyYCcw5fxtO4QQeVLKnJbaqRWBQtFN2HqwyicCALk7y5i5eDUStwAMZwf/Nt+HBReU0ag8xFT7vWwXR/JDrZO5S9Z4istFoQnQPW2q7S62FVUzvH+fNumzw+Ugd38uj615jC0VWxqdzy/KZ9n5y9xlICQ+048SgI5FCYFC0Q3Qdcn8DwIzaMNCDGzaV40JK/nmq7HgABoLgJUQ0u0LgRAiQowgpS8PYH1hOWOSolm3273vQITZQFrfiMPrqyf0M8wQxqQlkwLKPjQkKyFLDfxdACUECkUXI1hZiJIaR4A9H6DG4SKMUjaYr0GjXgDALQI1hHCu/W62iRTwlIirdTgRQgTkAbx5xXiKquyUWR0M6xeJpv0+s5DD5SD3QC5Pr32aDSUbEIhGBd+8DIkawoITFviyfxWdS5sIgRBiEXAGcFBKOcpzLBZ4CxgE7AQukFKWCfe3/iRwGmAFLpNSBg8ZUCh6GcHKQmia8CVxrfmtFB33jmED2c135tuAxquA9XoyZ9f9g3Gpcay8KNudY1BQztjUGBIizY3yAPpFh9EvOux399vmtDH+jfEBs/+GImDGzEfnfoTBYFCrgC5GW60IFgPPAK/6HbsV+FJK+aAQ4lbP63nAqcBQz7/xwHOe/ysUvZ6iarsvHDR3ZykHK20IIRACXv/zUUxf8B21e9bzoGkhGdpuIFAEduoxTKu7l2Ji0YTg2T+OJbFPKEtnTwwY+IXgsPIA/DN/S22lXPnFlY1MQN4VQZghjJdPfpkR8SN+92pD0b60iRBIKb8VQgxqcPhs4DjPz68AX+MWgrOBV6U7XGmVECJaCNFfSrmvLfqiUHRXdF1y7ZtrfTkBLgknPv6Nz0E8rp+J18pmYDG7Q0UbrgJcwB/qniTUaERzwbhBsb7Bvi0TwJy6k0s+uYQNJRt8Gb8u6QpoMzpuNItPWczOqp0MiRqiBKCL054+gr7ewV1KuU8Ikeg5PhDY7deu0HMsQAiEELOB2QApKSnt2E2FomtQVGVn9c6ygGPVdhcaTobxG0vL5gf4ArwCYMPIpfbrWU0GoUYjdqckKyWaN68Y3ybmF2/Zh2JrMZWOSh7PfZzN5Zvd/fNk/oJ7BTAkegjPHf+cz/afFpN22M9XtD+d4SwO9pvZyKMkpVwILAR3HkF7d0qhaG+a2hvAe6642tboGndE0BwsNF4F2EQIZ9vuZituZ7DFpFFbpyOB9YUVlFrrDmsV4NSd/FLyC3esuIPtldubbGcQBjITM3nk2EeU7b+b0p5CcMBr8hFC9AcOeo73Uo6gAAAgAElEQVQXAsl+7ZKAve3YD4Wi02nKCQzgcLg4d8EPbNxbn9hlppI5fMhc8ydBVwFWYabymm1sffQ73zXLbjiW699e3yZVQR0uB8csOYZaV22z7cKN4fz3//6rkr+6Oe0pBB8ClwIPev7/gd/xa4QQS3E7iSuUf0DR02m4N4C3qJvD4WLMvf+j1j3hx4CDo1nHK+Ynfdf6i8BveizXa7fw3t+uoKY20C5vNBh+d1VQp+70beaOgGuXX9ukCAgEn57zKTXOGoZEK/t/T6CtwkeX4HYMxwshCoH5uAXgbSHETKAAmOZp/gnu0NFtuMNHL2+LPigUXRn/Gv7ZKdFIKXG5dM59/gefCJiwstk8C4PHUtrYGSywzlzN+ylxaJpGgtHIUYNiySso84WFCnFoTmGHy8GPe3/k+q+uxy7tzbYdFj2MG3Nu5Kh+R6mNX3oYqtaQQtFGNOUD8B6PtZgornFw7ZtrySsoZ0S/SDbsrUSgM4BCvjTfipnGiWEA0+03s5oMspJjefeqo31mpeb8Ds32VersrtzNmf85s8mkLw2NtJg0rsu+jqHRQ0kIT1Dmn26GqjWkUHQgDX0Ab8wcT0mNA4lk7tJ834Yx/zwvwxcZtGFvJaGU84XpdpI0d4mHhquAbXo0J9U9Abjt/T/trgjYK+BQwkK9m77rUueWb29psvQzuEs/PHbcY8SFqaqfvQElBApFG+DvA8jdVca0539oVBJizW+lnPD414A7MziFX/nafI/7dQMBkMBR9icpJh7/QLucQYfuBLY5bSzbtYxFGxbxa/mvzbYN1UL56JyPSAxXpR96E0oIFIo2INZiYnRSFOsLK8gYGOUr4uZPUrSJ3eV2UtnOUtMD9NPc4aINRWC2/Sq+YCLeP0+LSbD8xuPcfgGPH6AldKlz0HqQwspCLv+8ZTfcM1OeoW9EX9Ji05TztxeihEChOEy8ZqGfCsoZkxzFvy7KYuJDX/nOC9wz/H3lFXxqupFhmnul0FAAAI6wPwdEMS41hqcuzKS8tu6QCsE5XA5W71/N42seZ2vF1ibbZSVk8eDkB9ldtZucvjnK+dvLUUKgUBwmRdX1GcHrdlcgBYwZ2Me34YsRKxewnL+b3wSCO4Nfsk/i78wEwvjk2qMZmhjJ9uKaVouAw+Vg5Z6VXPPVNS22XXbuMl/m74DIAYf2ZhU9EiUECsUh0jBSp6Gh5i9vrGO9RwRCqGaLebbvXOO9AgTp9kWA2+E7JqkPQxMjyb5/GVU2J5GhRtbdcVLQHcN0qVNQWcCnv37KcxufazL6x8tzU55jYvJENftXNEIJgUJxCPhHB2UlR3HP2aMY1jfCF8+fMbAP6/dUYMDGyazmTtNioPEqQAdOtd/JVobh3StgzMA+vH/10Ww9UE2VzZ1cUGVzNtoxzKk72Va2jdu/vp1fq5t2/oYZwnjhxBfYX7ufE5JPwGhUf+6K4KjfDIXiEPCPDlqzq5zTnlpBZKiRvNtPpMTq4KrXczHrRWwwz/WtFBquAnTgSPtivCGhXl64dByappHWN4LIUKNvReDdMczhcvD9nu+55dtbsLka1yXy561T3mJ4wnA0TWMMY9rs/St6JkoIFIpDID4ihOyU6IAqoVU2J6sLSnnww/UYD65ho/kBoKnEsBtZTSYQaJ7JTon2yw3QWHfHSWwrqmZQfAgr9qxgT8Ue/pH3jxb79+yxz3J0ytHK/KM4JJQQKBStwOsXiA41MvfEoVzy4mrfNiwaTv7x4mv823wPFk9uV8NVwBa9H6fUPQSYAu4rgMyUaN6ZMzEgLLTaWcl7v/2LJZ8vabFvA8IHMO3IaVySfgkhIb+/0Jyi96KEQKFogH9JiFJrHdGhRi5YuLJRghiAERv55isJpw4IvgoYZ3+UYvoTrAL7J3OPYXj/Pj4RqLRXsjB/Ia/88kqL/fzf2f/DHGJW2b+Kw0YJgULhh9cZnLurDEuIgRqbk9AQDauj4TaMOsn8xqfmO7EQXAB26nH8oe5RvBFBDclKjmZ4/z7UOmt5d8u7VForWbB5QbP9S7GkMDd7LiekKuevou1Qv0kKhR9eZ7BLl77InYYiEEI1H5tuZIhWBQRPDBtnf4xi+tJwFRBqALsLslKieXXmGF5e/zKP5z/eYr9uy7qN4wcdT9/Ivmr2r2hzlBAoFH54y0Wv2VlKqClwJWDAwR/4kRfMzwHBVwGz7VfzBRPw/mmFGQW1znqFWH7TFH6r3MH7215l4tI5zfZFQ+OWrFu4YMQFmEymZtsqFIeDEgJFryVYCWchBG/MHM/5z//AT34+gRh2kGu+A29aV+PEMBjPa6QOiIa9Vb7r0vpGYDYZySvYQ7/UdZzz4b1YsTbbLw2N1096nfR+6aruj6JDUEKg6JU0Vza6pNpOvkcEjNiYxsf8w/wuEHwVMNWTGGYQGi9dOo4rXsllw95KwMaGivU8cGYGm8PupZKWef3E1xndf7QSAEWHooRA0SsJSAz7rZTzF/xAfmFgVFAE+/nZfIPvdfDEsEVAKJqAnEGxJESYMZisaFGfYOn/LQK4L//NZvtyydBLSI5K5ry085QJSNEpKCFQ9EriI0LITIoit6AcHQJEIIRq/sx/mGf+BAi+V8CF9r+yMWS875qMgVHcf+4Q/rnyabaHvYglzHOiGb/u05OeZvLgySr5S9HpKCFQ9Bp0XVJUZUcIiDIb2bS/KuC8QGcQW1huvq/+WKO9Ai7iC04BjHw0exJnP/st0rSH9VVb+L+PlyPwjP1NCMAfj/gjk1MnMyFpghIARZdBCYGiV6DrkgsXrvSVhggzadTW1UcEhVLOZ6YbSdFqgab2CngGiPW8qmHWRw9hGfZxYM3PIAIQTzx/GPIHbs6+mbCwsMYNFIpORgmBolewv7w2oD6QVwSM2Dibr3nU/CoQ3Bn8sP0knuMiwIDFsh1bxFdYYrdR5WkfMPZLfAeiTdG8fvLrpMSlqNj/TiZYhFh7XtfdUEKg6DE0/KP1vu4TYvDtFexPGKVsMtdv5BLMFzDYvgAwokWuIKz/FwgNLA3aByBgXtY8Thx0okr+6gBaM1A3jBBbMmsCmtaK7T5/53XdESUEih6B1/Tj3Sdg/lmjuPODDfy0u4JQk0ZtXb0Bx4CDY1jLYvNTQFOJYX/mC8ahxf0PS8Ja3/nmxvUHJjzAKUeeoko/NKC9ZtWtHaj9I8TydpVRUuPwVXptDv/rcneVUVxtJ7FPaNB+dPdVg/qNVfQIDlTZfKaf3IIKznzme985rxlIoDOA3Xxrvq3JxLByYKx2IySsISJume8eDcXC6xC+YNAFnJN2DiP7jlSx/0Foz1l1wEC9s7TJgdqbLe7tQ3xEiK9vzQ3g7pLjMazeWYpLl1zz5lqWzp4Y0P/DfX9dRUQ6TQiEEKcAT+IuzP6ilPLBzuqLonuj65KrXs9rto2ZSj433UiKVgM0FoBK4FjL8bj6bsPCv33XBfxteuz/QsD5Keczb+I8QkMbDzzdjfYcjH7vbLwldF0ipSQrOYo1u8pxSbhmyTqWBhmIhRAsmTWhkdmwpQFcCMHTF2Ux6YEvcUlYW1DeqP+H8/66kumpU6YwQggD8CxwKjASmCGEGNkZfVF0f4r8MoEb4g4J3cwv5jmkaDVu567nb80lYatB49g+Qzj6iBRcfbe5rxEEtPO7GdePuJ61F61l/h/m9xgRmPHCKiY+8CUXLlyFrje/73FL9yqqsiP9Qq28s3GjJgJm401df6DSxsFKW8A9grW58IVVTHpwOU4dvGNn7s5SVu4o5kBFbaPrNU2QEGn2CV0ws08wEiPN5AyKbbL/h/L+GhJMRBq+14afZ3vRWSuCo4BtUsodAEKIpcDZwKZO6o+im6DrkqJqOwKICw+h1FqHy+kK2jaMUr403Ub/IFVCq4Hzk/qxxxQCOALOuxvhi/45Kuoojko6isszLu9xG7+01Yzdf3abnRLN0zOySexjbnI23nAF0jC8NyvZvVmPwaA1ekbuzlJcnrFx/Z4KMpOjyd9djgD++OJqAMalRvPWlZOanGE3NPtc+Vou78yZhMGgNeqft/+xFhPF1Y1rUzV8f96+NrfK8q5oslNjWNvAZNXw8+yI1UJnCcFAYLff60JgvH8DIcRsYDZASkpKx/VM0WXRdckFC34gt6AcgEizEavDyYj+kQHtBDpD2cBnZre10ft3WAw8HN2HJEcdLyQmuMf6pv62BEwdMJV7j74Xi8XSRKPuT1P280PFX1BW7yxj0kPLyfEbwLziEmyAA9h6oIpcv/DedbvLmfb8St6ZUz+Y+0qEe0TAoAlyUmN484rxrP6tlBkv/ui7Pm9XYzOOP1LC3WeN5LSnVnieV8H5z6/k37Mn8seXfmw0AMeFhwQdmJsWtVXkFZSRMTCqSUHziub38473iWawz7MtTWpN0VlCEOzPL2D9I6VcCCwEyMnJaf+1kaLLc6DS5hMBgCq7e7+AjXurCDWCzemuD/SV6UbiNfevjBTwm6axIMLCp7Ex7mN4Z3Pu+/ivvIVw1/6fNmJar6j709SM9lDxCop3tu7yG8DiwkN89284wBVV2Zm7dB25u8oINxt93ynAT7sDB3N/0cpOieaZi7J95p7xg2OJMBup9lyfkdSHuPD6789/wJYS3+ZDmgCvNWx9YQXbiqqDDsDBTEnxEeag4lBUZWf1zlLALWjnL1jJu1c1FjSnLllbUI6miUafe1sJdGvpLCEoBJL9XicBezupL4puQmkDG6oGvn2DnU4Hp/A1z5kXA1Aj4JUIC69FR1Nj9JZyEN7/AE/0j+d1bcloBkecyqdXXNTrSj/4z9h/L15BKa62c82SdT5zR6zFFDBYvnnF+IABTgh8GwFZ61x8PPcY7vjPBtbvLidnUGzAANi8aAlG9Iskr6CMUKPG+j2VzHjhR19V2WuXrGVtQTljU2N46sKsAPOSl4ykKNL6RviJTQxSuk04wSKInp6RHVQ0GmrpT4X1gtaSSah177Xt6SwhWAMMFUIcAewBLgQu6qS+KLogDWdwRVV2kIE7hXlfWTjIevN1aMBBYH5sFN9H9alv2OCPyH8FcNPIu5gx5v+osOudHsLX3dE0QWKfUJb6DWDF1YErgFJrXcAABwQIw8j+fXh3zqSA7949+3Z/Nw3NTP4rjXW7y9ElWD3hwrk7S5m2cCXrCytweab9uTtLkUgsZiNVNicGz4ogK8Xtk9A0jSWzJlBUZefaJWuZ9OBy32y/YQSREASdtSdEmhmXGs2aXe7Vq1fQWmMS8tLRYaWdIgRSSqcQ4hrgM9zho4uklBs7oy+Kroe/UzAjKRoNSZ4nKijUADaPb9iAg5P5mifMi1lhDmGt0cCixPj6G/n9ATUMvLAWZzMy/BIuyTkeIQQJPcsH3K60NEj5D9bBTBxCBK5AGs58hcA3e27KYdrwnHel4d1r2mp3MiY5mp/8RADAYnYPeVaH55dICD6dewzD+kX63oumuQVnbUF5wGzfG0HkfWZCpDnorF0IwVtXTuJAlY3yGofv3sXV9hZNQsHeW0eElXZaHoGU8hPgk856vqLrUlLjYM3OUnTptrH64xWBcA6y2nwd74aFktMvOfAGTQiAtTQVqo5Brx0JGHhx1iS1AjhEDnWQao2JoynTVHMO04bn/FcasRYTpdY64sJNzHjhxwAzkNXhQhNuJ7P3PfiLgJemBKwp0QrGdUvzAz6n1tr9O9pRDCqzWNFF8M4yYy0mXLpOWIiBGnvjsNAI9jOfZ9gbv58J8X4C0Nzsv2gsb53zAOEWiy9KBEBTInDI/J5B6vf6IJobOFtaaXj/v2TWBA5W2jjp8W+psjuxhBiICw9pUZyaErDWvpemPqfW2P072lEMSggUXQB/U5DFbKTG7kRvMJiHUMr4qNeYWbeGa1MGAnHuEwG1H+pDz6xFw8GRhl41DjAx/cW15AyK4ahBMeR5nIbtPcvqiXTkINXcaqK1zlRNExgMGlaHO5rIandSaq0jIdLcbgIGTX9OrblnRzuKAURHZK0dLjk5OTI3N7ezu6FoJ4qq7Ex84EucQbNaS4nstwCiG2QONyj+4w0JdZalYTswHQhvdCejJvj+1uPRhFCO4cOgq9THaS1SeuL6PYPy0tkTOqTfXeFzEkLkSSlzWmqnVgSKDsU/M9gbA+6dPa3ZWYoAXFJHGA4gYj8iPG47vnl+sDKhCHRdULtvKnrVMUB97LgAMlOiMQp3wtDY1BgSI4NHaShaT1uEm3YknTHDhu71OSkhUHQYTZUREELwxPRM1u7ey7UfPYsl5iu0UCeiWQGAmqJRUDUZ3ZFCw7JZkWYjy244lsQ+oUhJp8/MFJ1LdxqUOwMlBIoOo6ja3qiMwDnPrqCOOraUrcKSuhRLf/89f4MLABXxVO2bBUQ3ekZmchQPnDOaYf0ifWWhm4vsUCgUSggU7YzXFISUXLNkHfUpYQ60sALW740hYvgjWPoE2fS9gf9qUJHg55Jb8RcA/xIBowb24b2rJql9ARSKQ0QJgaLdaGgKclOBlvA+lrhfAtqKJgTg+oPFpDldXFz5MD+TGHDNmIGRmENM5O0qIyMpinc9maEKheLQUEKgaDe8sdSgIwwliIg1WPp/6zsvRH29n4az/8tLSrm6soZL7HO5l3G4E9DrGZPUh/evPhpdh21F1aT1jVAioFD8TpQQKNqEYNFAFrOT5NR8DvIRWmi1r63/7F/4Bf//qaSU9DoXJ9fa0IAj7S8QLAz007nHMLx/H6SEP77UNXZ4Uii6M0oIFIeNrkumP/+Dr8hWxiCNcaNyeXv72xAGmmxU9y1gBXBOWTm3VVQR6jk03T6X1UFWAQBZyVEM79+nUe2WjkrFVyh6IkoIFIdNUbWdNbtKEYb9iJhl7AjdxG/b68/71/33hoQKKbmstIyrK2vwDt21CEbaXwKa3gJywcVjfSGgnZGKr1D0RJQQKA4Lh8vBt7u/xDL4HrSQ4Pu+ugXALQJ37S9itNNJmtOJhtsq9LE9nae4gK0ciX8+wJiBkSyZOYFznv+BLQdqOGpQDIl96kWisxKFFIqehhICxe/C5rTx6Y5PuWvlXQBoIY3NP17rj0Ayo7SM6yuqCfNbHUjABVzDrQQzA23YW0WNS/LpX6c0OdirRCGF4vBRQqBoNbrU2VO1h2U7l/HYusfcBz2bvAfd9tEGN1QXc1GVFbN7SRBwfrr9GlYznmAiADRZv16hULQtSggULeJwOVi1bxX/XP1PdlTtCDwZTACKjuT92m8Y7NLdJqEGbR62n8lznAuYsZg0rHU6YwZGEmI0kFdQTkZSFM9fPJbEPqHK3KNQdABKCBRNUmmv5IV1L7B4y+Im2/gEQEJdwbl84nqRwaIACL5KOMK+EIjwvbY5df7318kM6xepagIpFJ2EEgJFALrU2Ve9j+8Lv+e+1fe12D5GxHJg+/9xnmMr/zA/EWAmgnoRmG8/m1c5BwiM7Mnx2yFK1QRSKDoHJQQKwGP+2buKh358iIKagqBtvNE/ADV7zkBaR+Jyudhi/iveGNCGq4A6BGn2BUAkAGEmgd0pGZMUzYKLs5X5R6HoAigh6OVY66y8v/V9Hsx9sOlGnggfqYN192XotUPRkIxmEx+Y3dcFWwVMtd/OVkbiHxKqCY3v502hX5RbAHRdUlxtV+YghaITUULQC7E5bXyz+xsiDZFc+dWVLbavOXA01GSgO5IBDTOVrDX/BQvuPYUbrgJ04Ej7i4Cl8b0cLipq6+gfHXbIG6ErFIr2QQlBL8LhcrCicAV//fqvTbbxmn+SwpLQy85hy85+eMM7LUYnQ5wb+cD8ABBcAGbYb2E1o33XaEB2ShSb91dT43ARGWokra/bWfx7NkJXKBRtjxKCHo4udUptpZg1M0cvPRqJbLKtlOCqjaFu72wenXMGpz/9PQACnX4cYEXI39AMNvexBiIw3X4jq8nEPycgJyWKf12cQ0KkGZdLNqoSqkpEKBRdg8MSAiHENOBuYARwlJQy1+/cbcBM3Mmjc6WUn3mOnwI8iXvEeFFK2YxxWvF78Ub/XPPlNWyr2NZi+xjrpewu7Id0RZOVHENMmHvvXzOVfGb6G6laCehNmYEW0bA+0KgBfXjrykkYDO5B32gUDO/fJ6CNKhGhUHQNDndFsAE4F3je/6AQYiRwIZAODACWCSHSPKefBU4CCoE1QogPpZSbDrMfCg82p41lu5bxbO6zFNoKm2378gkvU1pXyvCICRz7z+98x38qLOcvS/KJZC/rzTcBwZ3B/qsATUCoScPqcO9Btnl/FaXWuhZNPapEhELR+RyWEEgpNwPBZnJnA0ullHbgNyHENuAoz7ltUsodnuuWetoqITgMdKmzt3ovuftyuXPlnS2272+7lh27+vOIrY7XLj+BrL9/EXBekzZSC9/jPfOLQONVgBVIt7+ML2YUGNk/kvfmTGL6iz+yvrCCHGXqUSi6De3lIxgIrPJ7Xeg5BrC7wfHx7dSHHo8udQ7UHODqz69mW1XL5p8XTnyBQeEZHPPw1z4H7ZqCUmoc7ugfAw4m8jOvmv/pyxcQDYrEnWq/ly0MxiA0XH7uhk17q6iwu3h3ziRl6lEouhktCoEQYhnQL8ipv0kpP2jqsiDHJP4B5YHHgz13NjAbICUlpaVu9ip0qbO/Zj9zl89lS9mWphtKkLqBgXV/4aM/X47JZERK6XPQZqfE8MQXWxHoDGAP35rn+b6ghquALXoUp9Q9BZg8fQh8VGZKtCoQp1B0U1oUAinlib/jvoVAst/rJGCv5+emjjd87kJgIUBOTk7ToS69CO8K4Npl17KlohkBAOaNuYe7/1OM09af7ZqBUqsTTXMRazHx1IwsBO6dxY576GM+Nd3KMK0ICO4MHm//J8X0w1/fM1OiMWnCVyTunTkT1QpAoeimtJdp6EPgTSHEY7idxUOB1bhHkqFCiCOAPbgdyhe1Ux96FE7dySWfXsLPxT8HPW/CxH1H30dMaAzj+49H0zT+++Mq38z/mjfzyNtVjsVsoLZOZ2xKDCHWEjaHzAQaO4OtGLjcfhOrGUWYwYAndwyArORoFvwxm/gIM6XWOmUGUii6OYcbPnoO8DSQAHwshMiXUk6VUm4UQryN2wnsBP4ipXR5rrkG+Ax3+OgiKeXGw3oHPRSn7mRr2VYMGDgy+kgu/ezSJkVgROwIlpy2BIMhsK6/NzTTpetMeGA5ANV2F0ZsxO/6mmdC3MFeDVcB6/VU9pz7EW+MGkBprZM5r+WybneFuy0gkRz90Fe+bGAlAgpF9+Zwo4beB95v4tz9wP1Bjn8CfHI4z+2p6FKnyFpEsbWYy/53GTbdnbxlMVqwOW0BbcMMYSyeupgESwLxlvigg7E3NPNgpftaDScj+ZX/muurivqLgNsM9ASDU9NYkpFEqbUOpPSJAMCwvhH8vKcSl8oGVih6DCqzuAvgFYDrll/HhtINjc5bnVZGxI1ga+lW0uPSuXPCnaTFpPkydBvdT5cUVdsRQJTZyLYDVUxMCuOFoumE4wAarwI26X05ve4RNIx8dFE2F734I3m7yhg1MDAJ7JcD1USGGrE6XCobWKHoISgh6GR0qfPnz/5M3oG8JttEmCJ489Q3KXeUExca16wpRtclFy5cyeqdZYB7FZDGbt4x30O4cPjcvfU5AQam2B+jmHhAkJkSjSaErwbQz3sqyUqO4qfdFeiea612Jx/PnezbR0ChUHRvlBB0MN7aP94BvdRWSv7B/KBt06LSuP+Y+0mLdc/+48PiW7y/t5AbgAkr+earsXhXAZ42Urp9v6fZ70WPHUWx3W06ykyuj/7xrwH05hXjKalxcM2Sdaz1HFMioFD0HJQQdBBO3cnW0q3cs/IetpRtITMxk0VTFxEXGkdmYqZvRZAem87dE+8mNiyWBEtCqwdbXZeU1DiICzdx1IAwYvZ8ztPm59Bwm4G8KwApYas+gKl1DwJGtDIbWcnRPHdxNn39NolpWAMosU8oS1VdIIWiR6KEoB3xzv4jTZFMeWsKNc4a37n8g/mU2kqJD4tn0dRFlNSWABAfFtzx6x3ogw3CXnPQmp1lZMe4eKf2T412DANwSvhJP5Lz6u7Bm9unS/h5TwUGTQu4b7AaQKoukELRM1FC0A44dSfby7dz/6r7+anoJ8wGM7Wu2oA2w2KHERcaB7h37UqwJDR5v4YbuLwxczxlte74fSnhl/2V5O08wDH8zKvWfwJ+zmDvTQxhnOB6jF11fYg0m/ji+snMfesnn6lHOX0Vit6LkLLrJ+3m5OTI3Nzclht2AZy6k8lLJ1NdV91kmzAtjJUXrWwU99/UrL+oys7EB77EqUsMmmBk/0g27a1kbGoMQkoKdm3hO/P1vp0A/E1BLqB8+ufEDx+HUydgT4DmVhkKhaL7I4TIk1LmtNROrQjamB0VOxqJQIQpgpq6GobFDuPeifcyLHZYo9DP5rZt9G7gkrurjFCTxs97KgHI21nE2yH3kGXejiDYZjE3s5oMfhyYAZqGUSNgTwBl6lEoFKCEoM0ZEjWECFME1XXVRJgi+ODsD4gLi6PMXtZs6Gdz2zZ6N3DZeqCK0576DoFOIiUsNj/CcAoblYfQgdH6Yqy4zT3XLs1nqdoPWKFQNIESgkNElzrFtcVoaMSFNR7YNU3juwu/Y0fFDoZEDanflrGF0M+Wtm3UNMHQxAjGDrBwR9FcMkQB0HgV8AvJnOH4ByP6x7BpXyW6hLUqA1ihUDSDEoJW4NSd7KjYweA+g5n5+UzWHlwLwNi+Y1k0dRGaCDTzGDUjaTFpwW7VJA23bXTv8VsVYM//0/Pf8XLxdMI1e0CdbylhvZ7CzLp5FBMNCDbsrSQ8xIDNqStnsEKhaBYlBC3g7/wNN4ZjdVp95/xDQNsCr83e4XCRdf8X1NhdRIYaWXfHSZTV1HLH/msIF3ZP4Td8IUFr9SGcV3c3Dbd7qHG4+N9fVQawQqFoHiUEDfDG/seYYyizl1FSW8bvyk8AAAvdSURBVOJz/tY4axgeO5xfSn8BIDMx0xcC2mbP1yXnPf8DNXYXGk7623bz674yhn82nXitwC0CEmowc579TkqIIWlgKkeZDOQVlBNm0qi2u2tGR4YaGZoYoURAoVA0ixICD7rUKakt4aZvbiL/YD4Wk4VaZy2ZCZmEG8OpcdYQYYpgyWlLKLWXNukjOFxKahxs3FOJERv55qsJx4b1pbvBUydIStikp3B63f3gCRgt21fFD7cejyYELpfO0Q9/hUuXWB2uVm0gr1AoejdKCKgv/JZ/MB+Xe9sE3yogvyifz877jApHhc/5m2hJbPs+eEtEWAxMHVjHo8VzsOBACLDIWuoSMzAVb2KrYQhnVd9BhNnkm/mPTY0hMdKMEAIpJTnNOJ0VCoWiIUoIwFf4zSsCAkG4Kdy9IkjMJNGSSN/wvu32fG8OwbpdRXxk+Tv/cm4BgZ8ZKBTrjE9JNFkZGhbPKmsdsRYTxTXuVUKCRwTwtPduRel/XKFQKJpCCQH4Cr/lH8wnMzGTR459hNjQ2BZj/w+F5rJ4S6ptFOzaxr8NjzC0bldAeQgrIfw54d+8FR0OIgINfKaevn1CGz2jYVKa0gGFQtESvUIIGpZ+bogQgkVTFzVq01bRQM1lDaPrxL9zLj+E/AAyMC+gLm441ku+4q2osFaJUXNJaQqFQtEUwbe46kF47f8n/vtELv/scnSpB22nCa3Jyp+HS0mNg9ydpTh1Se7OUkpqHPUnrcWIwh99JSIk7oqgP4kjMVz1PQnRllb3yZuUZtSE8g8oFIpW0+NXBP72/7aO+28tsRYTFrORKpsTS4iAqgPI8CSEpkF4AiRPgF0/IJGs1QdzpeNGykQ0q2wuEkyt/4oaJqUp/4BCoWgNPV4IGtr/2zruvzWUWuuoddTRl2IW6k8Q/fwuNpvTGT7vGzSDAS79CKoPAvDwmzsoLygn53fO6P+/vbuPrauu4zj+/tx2hZXNjW7UQdduGMbcQxDkaYYYw5NOWSAaTQAflmBCoiziQyIsSzSGzIeQoDGQIKJi4uayKETkQRgR5A9hgDDnSre5jEDLgD2UueEdW2/P1z/u6Xa33bbDlp7bez6vpNk999z2ftL13u89v+/v/I4XkjOz9yoXy1AP1yMYbcc2hiPpp+uHH2deXydQHgIqRYG9X9vI9BntQ36vmdn/y8tQVxgY/x8LlY3hCzqmsPr6syhEiXmlzqMawa9M+BBntbYd/p6BN39/ojezsZaLQjCWBmbu9Cf9fGvHt9FP/w2NR6Z5ls8LaOIDX/8bSheTG3RGkZnZGBjRrCFJt0vaLGmjpAckTa3Yt1zSNklbJH2q4v7F6X3bJN06kuevRdMnNXFh+2QWFTZzfmELin6i77+HF4rrig5uaL2f1lNPAapP+TQzG0sjPSJYByyPiJKknwDLgVskzQeuBRYAZwBPSBpYl/ku4EqgB3he0oMR8fIIc9QMJf2s3ns9NO0DNRCRUNRETkoOsG3CXKYtO/q8gOGuQ2Bm9n4bUSGIiMcrNp8FPp/evgZYExEHgVckbQMuSvdti4jtAJLWpI+tm0LA7q1wcF+6PEQ/ry1Zy+X3H2Jqsp+9fVN4pqHhqCawp3yaWdZG84SyG4BH09ttQHfFvp70vsHurxvJtLkU1UwE7KeZS/9wiIlNTbxdmMr5s1qqfuIfaBC7CJhZFoY9IpD0BDCjyq4VEfGn9DErgBKwauDbqjw+qF54qs5flXQjcCNAR0fHcDFrxp4DJS45+AtmJzvYShtQoHiwxMPf8AVizKw2DVsIIuKKofZLWgosAS6PIycl9ACVE+RnAjvS24Pdf+zz3gPcA+XzCIbLOWaShGT/W/QW+5j2wfTs4ArTJzVx3qzTeOHVRiY3NVA8WOKC2S0uAmZWs0bUI5C0GLgF+EREFCt2PQislnQH5WbxHOA5ykcKcySdCbxOuaF8/UgyjKkkIX5zFXT/nZaArqaFfPjWp8tnB6cqx/xbmifQW+zz2L+Z1bSR9gjuBCYD6yRtkHQ3QER0AmspN4H/AtwUEf0RUQKWAY8BXcDa9LGZS5Jg1/6DVDvTOin1sWf7S8T+t6BnPQWgIDj70Mv07jr+gGZgzL+hoeCxfzOreSOdNXTWEPtWAiur3P8I8MhInne0DXVSV1Lq48DKDlqSIsVCM81tF5L0PAsBW5vmM6+1rnrdZpZDPrOYodfxf/u1TbQkxfIlI5MivZf+iFOnn05vsY95VXoEZmbjjd/FOGYd//Yp8M5b9Pf1sfvNbk5tX0ixUJ4OWiw0M7XjHPYUWpg2o91FwMzqQi5WHz0RSRLs2neA3XddydmHOjmgiTTHu2xpWsBtU25j7+tbmDxzAWpo5MXXvC6QmdU+rz76HhUIGnu3MPdQJ40KGqM8HHT2oU62v/4GO6Odhp59INHvS0GaWR1xIQBIEvjtElq611MsTCSSIgfUzMR4l60nLWD2jFn0dv+Hj3ZMBYkXvS6QmdURFwKA4m7oXo+SEs0F6F36FFPbF/L2njeZ39rGGnR4LaAIvC6QmdUVdzshvW7wxVBoRO0XM+3Mc2mYMIHpaUO4ci0grwtkZvXGRwRQvnbk0ofKRwannAZ+kzezHHEhGFAowKTWrFOYmY25fAwNJQm8s7N8nUgzMztK/ReCdEYQd8yD+64qb5uZ2WH1XwjSGUEkpfK/xd1ZJzIzqyn1XwgqZgTRfnF528zMDqv/ZrFE8pU/07trB9Na2zzt08zsGHV/RJAkwXX3Psein/+La3+5niRxw9jMrFLdF4JqS0ybmdkRdV8Ijlpi2usDmZkdp+57BJXXEPb6QGZmx6v7QgBHriFsZmbHq/uhITMzG5oLgZlZzrkQmJnlnAuBmVnOuRCYmeWcC4GZWc4pxsEa/ZJ2Aa+O0o+bDoyHJUidc3Q55+hyztH1fuWcFRHDrrQ5LgrBaJL0QkRckHWO4Tjn6HLO0eWcoyvrnB4aMjPLORcCM7Ocy2MhuCfrACfIOUeXc44u5xxdmebMXY/AzMyOlscjAjMzq5DLQiDpNkkbJW2Q9LikM7LOVI2k2yVtTrM+IGlq1pmqkfQFSZ2SEkk1NUND0mJJWyRtk3Rr1nkGI+nXknZK2pR1lqFIapf0pKSu9P/85qwzVSPpZEnPSfpnmvMHWWcaiqQGSS9JeiiL589lIQBuj4hzIuJc4CHge1kHGsQ6YGFEnANsBZZnnGcwm4DPAU9nHaSSpAbgLuDTwHzgOknzs001qPuAxVmHOAEl4DsRMQ9YBNxUo7/Tg8BlEfER4FxgsaRFGWcays1AV1ZPnstCEBH7KjZPAWqyURIRj0dEKd18FpiZZZ7BRERXRGzJOkcVFwHbImJ7RBwC1gDXZJypqoh4GujNOsdwIuKNiHgxvb2f8ptXW7apjhdl76SbE9KvmnydS5oJXAXcm1WGXBYCAEkrJXUDX6R2jwgq3QA8mnWIcaYN6K7Y7qEG37TGK0mzgfOA9dkmqS4dbtkA7ATWRURN5gR+BnwXSLIKULeFQNITkjZV+boGICJWREQ7sApYVqs508esoHxIvqqWc9agatclrclPheONpEnAH4FvHnOEXTMioj8d/p0JXCRpYdaZjiVpCbAzIv6RZY66vVRlRFxxgg9dDTwMfP99jDOo4XJKWgosAS6PDOf6voffZy3pAdortmcCOzLKUjckTaBcBFZFxP1Z5xlOROyV9BTlHkytNeMvAa6W9BngZOADkn4XEV8ayxB1e0QwFElzKjavBjZnlWUokhYDtwBXR0Qx6zzj0PPAHElnSmoCrgUezDjTuCZJwK+Aroi4I+s8g5F02sAsO0kTgSuowdd5RCyPiJkRMZvy3+dfx7oIQE4LAfDjdFhjI/BJyh37WnQnMBlYl051vTvrQNVI+qykHuBjwMOSHss6E0DaaF8GPEa5qbk2IjqzTVWdpN8DzwBzJfVI+mrWmQZxCfBl4LL0b3JD+mm21pwOPJm+xp+n3CPIZGrmeOAzi83Mci6vRwRmZpZyITAzyzkXAjOznHMhMDPLORcCM7OccyEwM8s5FwIzs5xzITAzy7n/AStTKTe4BbSUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22ebfd20438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X,y,s=5, label='data')\n",
    "plt.scatter(X,ransac_pred,s=5,label='ransac')\n",
    "plt.scatter(X,lr_pred,s=5, label='linear-regression')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7. Polynomial Regression\n",
    "* Sometimes relationship between variables & target is of higher polynomial degree\n",
    "* Transformer can be used to convert data to higher degree\n",
    "* Linear models can predict coef of these higher degree polynomials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_circles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [],
   "source": [
    "X,y = make_circles(n_samples=1000, noise=.04)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x22ebfd7dc50>"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22ec022f0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0],X[:,1],c=y,s=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [],
   "source": [
    "pol = PolynomialFeatures(degree=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_tf = pol.fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = LogisticRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [],
   "source": [
    "trainX,testX,trainY,testY = train_test_split(X_tf,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
       "          penalty='l2', random_state=None, solver='liblinear', tol=0.0001,\n",
       "          verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.fit(trainX,trainY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.984"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.score(testX,testY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.56153614,  0.08571121,  0.02482483, -8.77406605, -0.03769976,\n",
       "        -8.78295209]])"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8. Bias Variance \n",
    "<img src=\"https://github.com/awantik/machine-learning-slides/blob/master/bv.PNG?raw=true\">\n",
    "#### Bias\n",
    "\n",
    "* Fitting training data poorly, but produce similar result outside training data\n",
    "* we are building simple models that predicts terribly far from the reality but they don't change much from dataset to dataset.\n",
    "* Situation of underfitting.\n",
    "*  a linear regression model would have high bias when trying to model a non-linear relationship.\n",
    "\n",
    "#### Variance\n",
    "* Building complex model that fits the training data well but many not work similar way of other dataset.\n",
    "* Model is not generalized & is overfitting.\n",
    "\n",
    "#### Bias Variance TradeOff\n",
    "* Increasing the accuracy of the model will lead to less generalization of pattern outside training data. \n",
    "* Increasing the bias will decrease the variance. \n",
    "* Increasing the variance will decrease the bias.\n",
    "* We have to get perfect balance of bias & variance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](img/questions-01.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Linear Regression\n",
    "\n",
    "### 1.1 Conceptual Questions\n",
    "1. What is the difference between target and prediction? $\n",
    "\\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot $ ($\\star$)\n",
    "2. What is the loss used in standard Linear Regression Problem?  $\\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot$ ($\\star$)\n",
    "3. What is objective function in Linear regression? $\\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot$  ($\\star \\star \\star$)\n",
    "4. What are parameters being optimized in Linear Regression? $\\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot$  ($\\star$)\n",
    "5. What is the feature vector in Linear Regression $\\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot$  ($\\star$)\n",
    "6. What are linear models? Are they only about lines? $\\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot$ ($\\star$)\n",
    "### 1.2 Programming Questions\n",
    "1. Write a code to  $\\hspace{2 cm}\\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot $ ($\\star \\star \\star \\star \\star$)  \n",
    "  a. generate a 1000 points following $y=2x+3 + 0.1*U(0,1)$ where **'N'** is uniform noise between 0 and 1 and x is lying between -1 and 1.  \n",
    "  b. split the data into 8:2 ratio  \n",
    "  c. Fit the Linear Regression model over 80% training data and find train loss and validation loss.  \n",
    "  d. Plot the prediction and actual label for the given data in the same plot.\n",
    "  e. Plot the predicted line and actual line in a same plot.  \n",
    "  f. Use subplot to display **d.** and **e.** sidebyside.  \n",
    "  g. How do you explain extra 0.05 in the bias coeffecient?  \n",
    "\n",
    "# 2. Gradient Descent\n",
    "### 2.1. Conceptual Questions\n",
    "1. What is the gradient of a multivariate function $f(x,y)$? $\n",
    "\\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot $ ($\\star$)  \n",
    "2. Find the partial derivate of the bellow functions with respect to x and y $\n",
    "\\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot $ ($\\star$)  \n",
    "  $ \\begin{align}\n",
    " a)\\hspace{5pt}x^5 &&\n",
    " b)\\hspace{5pt}(2x+y^2)^2  &&\n",
    " c)\\hspace{5pt}ylog(x) &&\n",
    " d)\\hspace{5pt}(y-\\frac{1}{1+e^{-x}})^2\n",
    "  \\end{align}$  \n",
    "  \n",
    "3. Find the gradient of the bellow functions with respect to $ \\vec{x}=[x_1,x_2]$ for $x=(0,0), (1,1)\\text{ and }(0,1)$.   \n",
    "***Note : $\\vec{w}=[2,3]$ for the problem ***  \n",
    "  \n",
    "  $ \\begin{align}\n",
    " a)\\hspace{5pt} w^\\top x &&\n",
    " b)\\hspace{5pt}log(1+w^\\top x)  &&\n",
    " c)\\hspace{5pt} \\frac{1}{1+e^{-w^\\top x}} &&\n",
    "  \\end{align}$\n",
    "  \n",
    "4.  What is learning rate, step size and momentum in gradient descent. What do they signify in theory and in practice? $\n",
    "\\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot $ ($\\star \\star \\star \\star \\star$)  \n",
    "5. What is difference between stochastic gradient descent, batch descent and the standard gradient descent. $\n",
    "\\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot $ ($\\star \\star \\star$)  \n",
    "6. What is a Jacobian Matrix and Hessian Matrix?  $\n",
    "\\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot $ ($\\star $)  \n",
    "7. Write the pseudo code for gradient descent for Linear Regression.\n",
    "\n",
    "# 3. Polynomial Regression Introduction\n",
    "### 3.1 Conceptual Questions\n",
    "1. Is Polynomial regression special case of linear regression? If yes, what is the feature transformation used?  \n",
    "2. What does each of the coeffecient in polynomial regression represent? Slope, Slope of slope, etc.  \n",
    "3. What is the order and degree of polynomial?   \n",
    "\n",
    "# 4. LASSO AND Ridge Regression\n",
    "### 4.1 Conceptual Question\n",
    "1. Find the Lp Norm with p = $\\frac{1}{2},1,2$ for the bellow vectors  $ \\hspace{2 cm}\\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot $ ($\\star \\star \\star $) \n",
    "  $ \\begin{align}\n",
    " a)\\hspace{5pt} [1,2,3] &&\n",
    " b)\\hspace{5pt} [3,4]  &&\n",
    " c)\\hspace{5pt} [4,3] &&\n",
    " d)\\hspace{5pt} [6,8,10,30,100] &&\n",
    " e)\\hspace{5pt} [1,10,100]\n",
    "  \\end{align}$  \n",
    "\n",
    "2. When do we choose Manhattan distance instead of euclidean. List atleast 3 reasons.  \n",
    "3. Why do we regularize weights? What is its impact on objective function?  \n",
    "4. What is a sparse solution? Why do we desire it?  \n",
    "5. What is the impact of strong regularization? How to choose a regularization constant?  \n",
    "6. Why does L1 regularization of weights give a sparse solution ?  \n",
    "7. How to theoratically find if the regularization is dominant or is it the rms loss function?\n",
    "\n",
    "### 4.2 Programming Questions\n",
    "1.  Write a code to  $ \\hspace{2 cm}\\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot $ ($\\star \\star \\star \\star \\star$)  \n",
    "  a. generate a 1000 points following $y=2x^2+5 + N(0,1)$ where **'N'** is standard normal gaussian noise with 0 mean, 1 standard deviation and where x is between -2 and 2.  \n",
    "  b.  Fit the linear equation, quadratic equation and polynomial of order 5.  \n",
    "  c.  Find out the number of iteration it takes to get a solution within $\\pm 0.01$ error margin for all the three cases.  \n",
    "  d.  Try to use L1 Regularization and find out the feature indices which had 0 weight coefficient associated with it in the solution. i.e in $ax^4+bx^3+cx^2+dx+e$, if a,e are 0, then $x^4$,constant are the redundant features.\n",
    "  e.  Select only 25 points out of 1000 points and fit the models mentioned in **'b.'** again.  \n",
    "  f. Use L2 regularization and observe if it gives a better solution after 200 iterations than its counterpart unregularized versions.\n",
    "\n",
    "# 5 Robust Regression\n",
    "### 5.1 Conceptual Questions\n",
    "1. Write the pseudo-code for RANSAC.  \n",
    "2. How is RANSAC different from Theil Sen? Which one gives faster convergence?  \n",
    "\n",
    "### 5.2 Programming Questions\n",
    "1. Write a code to  $ \\hspace{2 cm}\\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot $ ($\\star \\star \\star \\star \\star$)  \n",
    "  a. Generate a 1000 points following $y=2x+3 + 0.1*U(0,1)$ where **'N'** is uniform noise between 0 and 1 and x is lying between -1.   \n",
    "  b. Add 50 more points with equation   $y=2x+200 + 0.1*U(0,1)$ with x lying between -1 and 1. This results in a total of 1050 points.   \n",
    "  c. Compare the performance of Linear Regression and RANSAC for the same.  \n",
    "  d. Plot the points considered as inliers by the RANSAC with color1 and the outliers with color2.  \n",
    "  e. Plot the left and right margin for RANSAC line fit along with the points.  \n",
    "\n",
    "# 5 Logistic Regression\n",
    "### 5.1 Conceptual Questions\n",
    "1. What is the decision boundary in Logistic Regression? What is the order of the equation to represent decision boundary for a feature vector of dimension n?  \n",
    "2. How is classification different from regression. What are the different ways to convert binary classifier into a multiclass classifier?  \n",
    "3. Why did we use sigmoid curve instead of heaviside/step function?  \n",
    "4. What is entropy of a probability distribution?  \n",
    "5. Write down the binary cross entropy loss for logistic regression.  \n",
    "6. Why do we use cross entropy loss instead of root mean square loss?  \n",
    "7. What is catagorical cross entropy loss? How is it different from binary cross entropy loss?  \n",
    "8. What is difference between self entropy and cross entropy. Which one are we using for loss?  \n",
    "9. Why is the output of logistic regression called logit?  \n",
    "10. What is the target/label/actual output  and behavior/logit/predicted output ?  \n",
    "11. What is it that we are trying to learn ? Why do we call classification/regression as a function approximation problem?  \n",
    "\n",
    "### 5.2 Programming Questions\n",
    "1. Write the code for the following.  \n",
    "  a. Generate a set of 1000 points in 2D with centers as (-2,0) and (2,0) and standard deviation as 0.5.  \n",
    "  b. Shuffle the data and select 80% of data for training and 20% for validation  \n",
    "  c. Plot the training data  \n",
    "  d. Find the accuracy for Training and Validation  \n",
    "  e. Do the steps from a. to d. with 3 centers instead of two.i.e. (-2,0),(-6,0) and (0,2). Here points via center (-6,0) and (0,2) belong to the same class. Check the performance of the Logistic Regression. Explain the change in accuracy for validation data.  \n",
    "\n",
    "\n"
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